Proposed Problems - Table of Content (Page 1 of 6)
NCTM Processes: Problem Solving, Reasoning & Proof, Communications, Connections, and Representation

Proposed Problem 424.
Triangle, Cevian, Angle, 90 degree, Congruence.

Proposed Problem 423.
Triangle, 30, 40 degree, Angle, Congruence.

Proposed Problem 422.
Triangle, 24, 30 degree, Angle, Congruence.

Proposed Problem 421.
Right Triangle, Cevian, Angles, Measurement.

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

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

Euclid's Elements Book I, Proposition 1: On a given finite line to construct an equilateral triangle

Proposed Problem 420.
Triangle, Altitude, Angles, Sides, Measurement.

Proposed Problem 419.
Triangle, Cevian, Incircle, Excircle, Inradius, Exradius.

Proposed Problem 418.
Triangle, Incircle, Inradius, Equal Tangent circles, Radius.

Related Geometry Topics:
Computational, Manifold, Topology, String theory, Coordinate, Analytical, Trigonometry, Projective, Algebraic, Differential, Symplectic, Lie theory, Fractal, Dimension theory, Computer graphics, Atiyah, Gromov, Perelman.

Proposed Problem 417.
Tangent circles, Tangent lines, Angles.

Routh's Theorem 1.
Triangle, Cevians, Ratio of Areas.

Routh's Theorem 2.
Triangle, Cevians, Ratio of Areas.

Routh's Theorem 3.
Triangle, Cevians, Ratio of Areas.

Routh's Theorem 4.
Triangle, Cevians, Ratio of Areas.

Proposed Problem 416.
Triangle, Cevians, Trisectors, Area.

Proposed Problem 415.
Right Triangle, Cevian, Angles, Congruence.

Proposed Problem 414.
Triangle, Angles, Altitude, Median, Congruence.

Proposed Problem 413.
Cyclic Quadrilateral, Orthocenter, Parallelogram, Concurrency, Congruence.

Proposed Problem 412.
Triangle, Cevian, Angles, Congruence.

Proposed Problem 411.
Triangle, Median, Angles.

Proposed Problem 410.
Two Regular Pentagons, Angle.
Puzzle: 22 piece polygons.

Proposed Problem 409.
Quadrilateral, Diagonals, Perpendicular, Congruence.

Proposed Problem 408.
Cyclic quadrilateral, Perpendicular, Parallelogram, Congruence.

Proposed Problem 407.
Circle, Angle, Tangent, Perpendicular, Secant, Radius, Center.

Proposed Problem 406.
Right triangle, 15 degrees, Midpoints, Congruence.

Proposed Problem 405.
Quadrilateral, 60, 75, and 135 degrees, Midpoint.

Proposed Problem 404.
External Equilateral triangles, Congruent and Concurrent Lines.

Proposed Problem 403.
Circular sector, 90 degrees, Circle, Semicircle, Area.

Proposed Problem 402.
Hexagon, Triangle, Centroid, Parallel, Congruence, Similarity.

Proposed Problem 401.
Area, Triangle, Angle bisector, Circumcircle, Perpendicular bisector, Congruence.
Puzzle based on poblem 401.

Proposed Problem 400.
Triangle, Angle bisector, Circumcircle, Perpendicular, Congruence.

Proposed Problem 399.
Right triangle, Midpoints, Distance, Pythagorean theorem, Congruence.

Proposed Problem 398.
Parallelogram, Area, Similarity, Congruence.

Proposed Problem 397.
Triangle, Altitude, Midpoints, Congruence.

Proposed Problem 396.
Square, Angle Trisectors, Congruence, Area.

Proposed Problem 395.
Square, 15 Degree, Equilateral triangle.

Proposed Problem 394.
Square, 90 Degree Arc, Diagonal, Congruence.

Proposed Problem 393.
Triangle, Orthocenter, Circumcircles, Congruence, Collinear.

Proposed Problem 392.
Triangle, Parallel lines, Concurrent lines.

Proposed Problem 391.
Triangle, Parallel lines, Collinear points.

Proposed Problem 390.
Triangle, Parallel lines, Collinear points.

Proposed Problem 389.
Triangle, Parallel lines, Harmonic Mean.

Proposed Problem 388.
Triangle, Angle bisector, Perpendicular, Parallel.

Proposed Problem 387.
Triangle, Angle bisector, Perpendicular, Concyclic points.

Proposed Problem 386.
Triangle, Angle bisector, Perpendicular, Parallel, Semiperimeter, Congruence.

Proposed Problem 385.
Triangle, Angle bisector, Perpendicular, Parallel, Semiperimeter.

Proposed Problem 384.
Triangle, Angle bisector, Perpendicular, Parallel, Semiperimeter.

Proposed Problem 383.
Concave Quadrilateral, Angle Bisectors, Semi-difference of Angles.

Proposed Problem 382.
Concave Quadrilateral, Angle Bisectors, Semi-sum of Angles.

Proposed Problem 381.
Quadrilateral, Diagonals, Angle Bisectors, Semi-sum of Angles.

Proposed Problem 380.
Triangle, Excenter, Parallel to a side, Angle, Congruence.

Proposed Problem 379.
Triangle, Excenter, Parallel to a side, Angle, Congruence.

Proposed Problem 378.
Triangle, Incenter, Parallel to a side, Angle, Congruence.

Proposed Problem 377.
Triangle, Internal Angle Bisector, Altitude.

Proposed Problem 376.
Triangle, Excenter, Internal and External Angle Bisectors.

Proposed Problem 375.
Triangle, Excenter, External Angle Bisectors.

Proposed Problem 374.
Triangle, Incenter, Internal Angle Bisectors.

Proposed Problem 373.
Square, Inscribed Circle, Diagonal, Perpendicular, Angle.

Proposed Problem 372.
Circles, Common Internal and External Tangent, Angles.

SAT Math Practice 1,
Video.

Proposed Problem 371.
Square, Inscribed circle, Triangle, Area.

Proposed Problem 370.
Triangle with squares, Circumcircles, Tangent circles.

Proposed Problem 369.
Intersecting circles, Chord, Center, Angle, Congruence.

Proposed Problem 368.
Triangle, 120 degrees, Angle bisectors, Perpendicular.
Puzzle problem 368.

Proposed Problem 367.
Square, Angle, 45 degrees, Pythagoras, Congruence, Similarity.

Proposed Problem 366.
Scalene triangle, Circumcircle, Angles, 60 Degrees, Equilateral triangle.

Proposed Problem 365.
Circular Sector of 60 degrees, Midpoints, Perpendicular, Congruence.

Proposed Problem 364.
Obtuse triangle, Congruence, Circles, Diameter, Curvilinear triangle, Area.

Proposed Problem 363.
Right triangle, Congruence, Angles.

Proposed Problem 362.
Circle, Chord, Perpendicular, Equal chords.

Proposed Problem 361.
Right triangle, Incircle, Incenter, Tangency points, Angle.

Proposed Problem 360.
Area of a triangle, Curvilinear triangles, Circles, Diameters.

Proposed Problem 359.
Cyclic quadrilateral, Angle bisector, Rhombus.

Proposed Problem 358.
Isosceles triangle 80-80-20, Circle, Angles, Congruence.

Proposed Problem 357.
Square, Exterior point, Triangles, Area.

Proposed Problem 356.
Square, Point inside, Triangles, Area.

Proposed Problem 355.
Circles, Common external tangent, Concyclic points.

Proposed Problem 354.
Rhombus, Square, 45 degrees.

Proposed Problem 353.
Tangential quadrilateral, Diagonals, Incircles, Inradii.

Proposed Problem 352.
Tangential quadrilateral, Incircles, Common tangent, Circumscribable or Tangential quadrilateral.

Proposed Problem 351.
Rhombus, Incircles, Common tangent, Circumscribable or Tangential quadrilateral.

Proposed Problem 350.
Triangle, Cevian, Incircles, Tangents, Tangency Point, Angles.

Proposed Problem 349.
Triangle, Cevian, Incircles, Tangents, Tangency Point.

Proposed Problem 348.
Circles, Common External Tangents, Common Internal Tangent.

Proposed Problem 347.
Triangle, Altitude, Perpendicular, Circle, Concyclic points.

Proposed Problem 346.
Equal circles, Tangents, Hexagon, Semiperimeter.

Proposed Problem 345.
Equal circles, Tangents, Concurrent lines, Hexagon, Semiperimeter.

Proposed Problem 344.
Quadrilateral, Extension of sides, Circle, Tangent, Semiperimeter.

Proposed Problem 343.
Hexagon, Inscribed circle, Tangent, Semiperimeter.

Proposed Problem 342.
Pentagon, Inscribed circle, Tangent, Semiperimeter.

Proposed Problem 341.
Triangle, Inscribed circle, Tangent, Semiperimeter.

Proposed Problem 340.
Triangle, Angle Bisectors, Perpendiculars, Distances. Exterior Point.

Proposed Problem 339.
Triangle, Angle Bisectors, Perpendiculars, Distances. Interior Point.

Proposed Problem 338.
Triangle, Circumcircle, Inscribed Circle, Exterior angle bisector, Concyclic points.

Proposed Problem 337.
Isosceles Trapezoid, Angle bisector, Parallel, Concyclic points.

Proposed Problem 336.
Two equal circles, a Common Tangent and a Square.

Proposed Problem 335.
Cyclic Quadrilateral, Perpendiculars to Sides.

Proposed Problem 334.
Cyclic Quadrilateral, Perpendiculars to Diagonals.

Proposed Problem 333.
Circle inscribed in a semicircle, Perpendicular to the common tangent.

Proposed Problem 332.
Cyclic quadrilateral, Ratio of diagonals, Similarity.

Proposed Problem 331.
Square, Point on the Inscribed Circle, Tangency Points.

Proposed Problem 330.
Cyclic quadrilateral, Perpendicular diagonals, Area, Circumcenter.

Proposed Problem 329.
Triangle, Altitudes, Circle, Diameter, Concyclic points.

Proposed Problem 328.
Triangle, Incircle, Tangency Points, Parallel, Midpoint.

Proposed Problem 327.
Right triangle Area, Incircle, Circumcircle, Square.

Proposed Problem 326.
Equilateral triangle, Semicircle, Equal arcs.

Proposed Problem 325.
Isosceles triangle, Altitude, Cevian, Incircle, Excircle.

Proposed Problem 324.
Quadrilateral with perpendicular diagonals, Concurrence.

Proposed Problem 323.
Triangle, Incenter, Circumcenter, Equal circles, Collinearity.

Proposed Problem 322.
Square, Inscribed circle, Tangent, Triangle area.

Proposed Problem 321.
Triangle, Incenter, Excircle, Midpoint of the Altitude, Collinearity.

Proposed Problem 320.
Triangle, Circumcircle, Incenter, Excenter, Collinear points.

Proposed Problem 319.
Triangle, Altitudes, Perpendiculars, Collinear points.

Proposed Problem 318.
A Scalene triangle, Altitudes, Collinear points.

Proposed Problem 317.
Right triangle and Inscribed Squares.

Proposed Problem 316.
Circular segments and Inscribed Squares.

Proposed Problem 315.
Three Tangent circles, Common external tangent line, Geometric Mean.

Proposed Problem 314.
Tangent circles, Common external tangent line, Geometric Mean.

Proposed Problem 313.
Circle, Chord, Tangent, Perpendicular, Geometric Mean.

Proposed Problem 312.
Cyclic quadrilateral, Side extensions, Tangents.

Proposed Problem 311.
Circle Inscribed in a Semicircle, Chord, Diameter.

Proposed Problem 310.
Circle Inscribed in a Semicircle, 45 Degrees Angle.

Proposed Problem 309.
Regular Nonagon or Enneagon, Diagonals, Side.

Proposed Problem 308.
Regular Nonagon or Enneagon, Midpoints, Side, Arc, Angle.

Proposed Problem 307.
Regular Nonagon or Enneagon, Midpoints, Side, Arc, Angle.

Proposed Problem 306.
Square, Triangles, Angles, Sides.

Proposed Problem 305.
Square, Triangles, Angles, Sides.

Proposed Problem 304.
Triangle, Angle bisector of 120 degrees.

Proposed Problem 303.
Triangle, Angle bisector of 90 degrees.

Proposed Problem 302.
Triangle, Angle bisector of 60 degrees.

Proposed Problem 301.
Tangents to a circle, Secants, Square.

Mind Map of How to Solve Problems
George Pólya's 1945 book How to Solve It is a book describing methods of problem solving.