Geometry Theorems and Problems - Recent Additions (Page
9 of 15)
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Proposed
Problem 424.
Triangle, Cevian, Angle, 90 degree, Congruence. |
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Euclid's Elements Book I, Proposition 4: (Side-Angle-Side SAS) |
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Euclid's Elements Book I, Proposition 3: Given two unequal straight lines, to cut off from the greater a straight line equal to the less |
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Euclid's Elements Book I, Proposition 2: To place at a given point (as an extremity) a straight line equal to a given straight line |
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Euclid's Elements Book I, Proposition 1:
On a given finite line to construct an equilateral triangle |
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Proposed
Problem 423.
Triangle, 30, 40 degree, Angle, Congruence. |
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Proposed
Problem 422.
Triangle, 24, 30 degree, Angle, Congruence. |
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Proposed
Problem 421.
Right Triangle, Cevian, Angles, Measurement. |
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Proposed
Problem 420.
Triangle, Altitude, Angles, Sides, Measurement. |
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Proposed
Problem 419.
Triangle, Cevian, Incircle, Excircle, Inradius, Exradius |
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Proposed
Problem 418.
Triangle, Incircle, Inradius, Equal Tangent circles, Radius. |
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Proposed
Problem 417.
Tangent circles, Tangent lines, Angles. |
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Routh's Theorem - Index
Triangle, Cevians, Area, Ratio.
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Routh's Theorem 1.
Triangle, Cevians, Ratio of Areas. |
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Routh's Theorem 2.
Triangle, Cevians, Ratio of Areas. |
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Routh's Theorem 3.
Triangle, Cevians, Ratio of Areas. |
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Routh's Theorem 4.
Triangle, Cevians, Ratio of Areas. |
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Proposed
Problem 416.
Triangle, Cevians, Trisectors, Area. |
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Proposed
Problem 415.
Right
Triangle, Cevian, Angles, Congruence. |
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Proposed
Problem 414.
Triangle, Angles, Altitude, Median, Congruence. |
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Proposed
Problem 413.
Cyclic Quadrilateral, Orthocenter, Parallelogram, Concurrency, Congruence. |
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Proposed
Problem 412.
Triangle, Angles, Congruence. |
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Proposed
Problem 411.
Triangle, Median, Angles. |
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Proposed
Problem 410.
Two Regular Pentagons, Angle. |
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Proposed
Problem 409.
Quadrilateral, Diagonals, Perpendicular, Congruence. |
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Proposed
Problem 408.
Cyclic quadrilateral, Perpendicular, Parallelogram, Congruence. |
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Proposed
Problem 406.
Right triangle, 15 degrees, Midpoints, Congruence. |
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Proposed
Problem 405.
Quadrilateral, 60, 75, and 135 degrees, Midpoint. |
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Concurrent lines.
Theorems and Problems Index. |
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Proposed
Problem 404.
External Equilateral triangles, Congruent and Concurrent Lines. |
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Median of a Trapezoid, Theorems and Problems.
Index.
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Circular
Sector.
Index.
Theorems and Problems.
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Proposed
Problem 403.
Circular sector, 90 degrees, Circle, Semicircle, Area. |
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Proposed
Problem 402.
Hexagon, Triangle, Centroid, Parallel, Congruence, Similarity. |
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Proposed
Problem 401.
Area, Triangle, Angle bisector, Circumcircle, Perpendicular bisector, Congruence. |
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Points, Theorems and Problems - Index. |
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Proposed
Problem 400.
Triangle, Angle bisector, Circumcircle, Perpendicular, Congruence. |
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Proposed
Problem 399.
Right triangle, Midpoints, Distance, Pythagorean theorem, Congruence. |
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Proposed
Problem 398.
Parallelogram, Area, Similarity, Congruence. |
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Proposed
Problem 397.
Triangle, Altitude, Midpoints, Congruence. |
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Proposed
Problem 396.
Square, Angle Trisectors, Congruence, Area. |
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Proposed
Problem 395.
Square, 15 Degree, Equilateral triangle. |
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Kosnita's
Theorem.
Circumcenters, Concurrent lines. |
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Proposed
Problem 394.
Square, 90 Degree Arc, Diagonal, Congruence. |
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Proposed
Problem 393.
Triangle, Orthocenter, Circumcircles, Congruence, Collinear. |
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Median Index.
Theorems and Problems. |
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Proposed
Problem 392.
Triangle, Parallel lines, Concurrent lines. |
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Proposed
Problem 391.
Triangle, Parallel lines, Collinear points. |
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Proposed
Problem 390.
Triangle, Parallel lines, Collinear points. |
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Proposed
Problem 389.
Triangle, Parallel lines, Harmonic Mean. |
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Proposed
Problem 388.
Triangle, Angle bisector, Perpendicular, Parallel. |
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Proposed
Problem 387.
Triangle, Angle bisector, Perpendicular, Concyclic points. |
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Proposed
Problem 386.
Triangle, Angle bisector, Perpendicular, Parallel, Semiperimeter,
Congruence. |
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Proposed
Problem 385.
Triangle, Angle bisector, Perpendicular, Parallel, Semiperimeter. |
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Proposed
Problem 384.
Triangle, Angle bisector, Perpendicular, Parallel, Semiperimeter. |
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Proposed
Problem 383.
Concave
Quadrilateral, Angle Bisectors, Semi-difference of Angles. |
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Proposed
Problem 382.
Concave
Quadrilateral, Angle Bisectors, Angles. |
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Proposed
Problem 381.
Quadrilateral, Diagonals, Angle Bisectors, Angles. |
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Chord.
Index.
A chord of a circle is the line segment joining two points on the
circle.
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Proposed
Problem 380.
Triangle, Excenter, Parallel to a side, Angle, Congruence. |
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Proposed
Problem 379.
Triangle, Excenter, Parallel to a side, Angle, Congruence. |
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Proposed
Problem 378.
Triangle, Incenter, Parallel to a side, Angle, Congruence. |
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Proposed
Problem 377.
Triangle, Internal Angle Bisector, Altitude. |
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Proposed
Problem 376.
Triangle, Excenter, Internal and External Angle Bisectors. |
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Proposed
Problem 375.
Triangle, Excenter, External Angle Bisectors. |
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Proposed
Problem 374.
Triangle, Incenter, Internal Angle Bisectors. |
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Proposed
Problem 373.
Square, Inscribed Circle, Diagonal, Perpendicular, Angle. |
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Proposed
Problem 372.
Circles, Common Internal and External Tangent, Angles. |
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Proposed
Problem 371.
Square, Inscribed circle, Triangle, Area. |
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Proposed
Problem 370.
Triangle with squares, Circumcircles, Tangent circles. |
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Proposed
Problem 369.
Intersecting circles, Chord, Center, Angle, Congruence. |
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Proposed
Problem 368.
Triangle, 120 degrees, Angle bisectors, Perpendicular. |
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Proposed
Problem 367.
Square, Angle, 45 degrees, Pythagoras, Congruence, Similarity. |
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Proposed
Problem 366.
Scalene triangle, Circumcircle, Angles, 60 Degrees, Equilateral triangle. |
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Proposed
Problem 365.
Circular Sector of 60 degrees, Midpoints, Perpendicular, Congruence. |
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Proposed
Problem 364.
Obtuse triangle, Congruence, Circles, Diameter, Curvilinear triangle, Area. |
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Special Right Triangle
30-60.
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Special Right Triangles.
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Obtuse Triangle. |
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Proposed
Problem 363.
Right triangle, Congruence, Angles. |
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Proposed
Problem 362.
Circle, Chord, Perpendicular, Equal chords. |
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Euclid's Elements Book I Word Cloud.
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Mascheroni
construction with compass alone. Index
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Proposed
Problem 361.
Right triangle, Incircle, Incenter, Tangency points, Angle. |
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Proposed
Problem 360.
Area of a triangle, Curvilinear triangles, Circles, Diameters. |
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Proposed
Problem 359.
Cyclic quadrilateral, Angle bisector, Rhombus. |
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Mascheroni construction: Find the center of a circle with compass alone.
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Proposed
Problem 358.
Isosceles triangle 80-80-20, Circle, Angles, Congruence. |
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Euclid's
Elements, Book X, Lemma for Proposition 33 One page visual illustration. |
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Proposed
Problem 357.
Square, Exterior point, Triangles, Area. |
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Proposed
Problem 356.
Square, Point inside, Triangles, Area. |
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Proposed
Problem 355.
Circles, Common external tangent, Concyclic points. |
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Proposed
Problem 354.
Rhombus, Square, 45 degrees. |
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Proposed Problem
353.
Tangential quadrilateral, Diagonals, Incircles, Inradii. |
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Proposed Problem
352.
Tangential quadrilateral, Incircles, Common tangent, Circumscribable or Tangential quadrilateral. |
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Proposed Problem
351.
Rhombus, Incircles, Common tangent, Circumscribable or Tangential quadrilateral. |
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Proposed Problem
350.
Triangle, Cevian, Incircles, Tangents, Tangency Point, Angles. |
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Proposed Problem
349.
Triangle, Cevian, Incircles, Tangents, Tangency Point. |
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Proposed Problem
348.
Circles, Common External Tangents, Common Internal Tangent. |
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Proposed Problem
347.
Triangle, Altitude, Perpendicular, Circle, Concyclic points. |
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Proposed Problem
346.
Equal circles, Tangents, Hexagon, Semiperimeter. |
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Proposed Problem
345.
Equal circles, Tangents, Concurrent lines, Hexagon, Semiperimeter. |
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Proposed Problem
344.
Quadrilateral, Extension of sides, Circle, Tangent, Semiperimeter. |
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Proposed Problem
343.
Hexagon, Inscribed circle, Tangent, Semiperimeter. |
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Proposed Problem
342.
Pentagon, Inscribed circle, Tangent, Semiperimeter. |
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Proposed Problem
341.
Triangle, Inscribed circle, Tangent, Semiperimeter. |
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Proposed Problem
340.
Triangle, Angle Bisectors, Perpendiculars, Distances. Exterior Point. |
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Proposed Problem
339.
Triangle, Angle Bisectors, Perpendiculars, Distances. Interior Point. |
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Proposed Problem
338.
Triangle, Circumcircle, Inscribed Circle, Exterior angle bisector, Concyclic points. |
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Proposed Problem
337.
Isosceles Trapezoid, Angle bisector, Parallel, Concyclic points. |
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Tangent Circles Index
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Proposed Problem
336.
Two equal circles, a Common Tangent and a Square. |
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Proposed Problem
335.
Cyclic Quadrilateral, Perpendiculars to Sides. |
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Proposed Problem
334.
Cyclic Quadrilateral, Perpendiculars to Diagonals. |
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Midpoints.
Theorems and Problems |
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Proposed Problem
333.
Circle inscribed in a semicircle, Perpendicular to the common tangent. |
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Proposed Problem
332.
Cyclic quadrilateral, Ratio of diagonals, Similarity. |
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Proposed Problem
331.
Square, Point on the Inscribed Circle, Tangency Points. |
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Proposed Problem
330.
Cyclic quadrilateral, Perpendicular diagonals, Area, Circumcenter. |
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Proposed Problem
329.
Triangle, Altitudes, Circle, Diameter, Concyclic points. |
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Proposed Problem
328.
Triangle, Incircle, Tangency Points, Parallel, Midpoint. |
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Tangential or Circumscribed Quadrilateral:
Diagonals, Altitudes Theorem. |
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Proposed Problem
327.
Right triangle Area, Incircle, Circumcircle, Square. |
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Proposed Problem
326.
Equilateral triangle, Semicircle, Equal arcs. |
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Tangential or Circumscribed Quadrilateral:
Diagonals, Inradii Theorem. |
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Tangential
or Circumscribed Quadrilateral
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Six Tangential or Circumscribed Quadrilaterals Theorem. |
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Tangential or Circumscribed Quadrilateral:
Pitot Theorem. |
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Proposed Problem
325.
Isosceles triangle, Altitude, Cevian, Incircle, Excircle. |
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Proposed Problem
324.
Quadrilateral with perpendicular diagonals, Concurrence. |
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Altitude Index.
Theorems and Problems. |
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Proposed Problem
323.
Triangle, Incenter, Circumcenter, Equal circles, Collinearity. |
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Proposed Problem
322.
Square, Inscribed circle, Tangent, Triangle area. |
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Collinear Points. |
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Incenter.
Index.
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Proposed Problem
320.
Triangle, Circumcircle, Incenter, Excenter, Collinear points. |
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Proposed Problem
319.
Triangle, Altitudes, Perpendiculars, Collinear points. |
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Proposed Problem
318.
A Scalene triangle, Altitudes, Collinear points. |
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Proposed Problem
317.
Right triangle and Inscribed Squares. |
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Proposed Problem
316.
Circular segments and Inscribed Squares. |
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Proposed Problem
315.
Three
Tangent circles, Common external tangent line, Geometric Mean. |
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Polygons. |
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Proposed Problem 287:
Regular Octagon. |
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Octagons. |
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Proposed Problem 286:
Square, Midpoints, Octagon. |
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Proposed Problem 285: Circular Sector 90 degrees, Semicircles, Circle, Tangent, Radius. |
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Proposed Problem 284: Circular Sector 90 degrees, Semicircles, Tangent, Radius. |
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Proposed Problem
283: Circular Sector 90 degrees, Semicircle, Circle inscribed, Radius. |
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Proposed Problem
282.
Right Triangle, Cevian, Angles, Perpendicular, Congruence. |