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Online Geometry: Circles, Theorems and Problems
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Circles - Table of Content
(Page 9 of 10)
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![Circles](../geometry/circles_index_17.jpg) |
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Geometry Problem
812.
Four Tangent Circles, Common Tangent Line, Diameter, Area, Collinear Centers. |
![Trisecting a line segment, 4 circles](../school-college/p811-trisecting-segment-4-circles-one-line-1.jpg) |
Geometry Problem
811: Trisecting a line segment.
With four circles and one line. |
![Trisecting a line segment, 2 circles](../school-college/p810-trisecting-segment-2-circles-8-lines-1.jpg) |
Geometry Problem
810: Trisecting a line segment.
With two circles and eight lines. |
![Trisecting a segment with three circles](../school-college/p809-trisecting-segment-3-circles-4-lines-1.jpg) |
Geometry Problem
809: Trisecting a line segment.
With three circles and four lines. |
![Parallelogram, Perpendicular, Semicircle, Area](../school-college/p808-parallelogram-perpendicular-right-triangle-semicircle-area-1.jpg) |
Geometry Problem 808
Parallelogram, Perpendicular, Right Triangle, Semicircle Area, Diameter. |
![Right Triangle Area, Incircle, Semicircle](../school-college/p807-right-triangle-area-semicircle-incircle-1.jpg) |
Geometry Problem 807
Right Triangle Area, Incircle, Tangency Points, Semicircle Area. |
![Triangle, Circumcenter, Similarity](../school-college/p806-triangle-circumcenter-similarity-1.jpg) |
Geometry Problem 806
Triangle, Points on sides, Circumcenter, Similarity. |
![Parallelogram, Angle Bisector, Parallel, Triangle, Circumcircle, Circumcenter](../school-college/p799-parallelogram-angle-bisector-circumcircle-circumcenter-1.jpg) |
Geometry Problem 799
Parallelogram, Angle Bisector, Parallel, Triangle, Circumcircle, Circumcenter. |
![Parallelogram, Secant Line, Tangent Circles, Triangle](../school-college/p798-parallelogram-secant-line-tangent-circles-1.jpg) |
Geometry Problem 798
Parallelogram, Secant Line, Tangent Circles, Circumcircles, Triangle. |
![Right Triangle, Altitude, Incircles, CIrcumcircles, COngruence](../school-college/795-intersecting-circles-secant-chord-midpoint-90-degrees-1.jpg) |
Geometry Problem 795
Intersecting Circles, Common Chord, Midpoint, Tangent, Secant Line, Perpendicular, 90 Degrees. |
![Right Triangle, Altitude, Incircles, CIrcumcircles, COngruence](../school-college/p794-right-triangle-altitude-incircle-2-circumcircles-congruence-1.jpg) |
Geometry Problem 794
Right Triangle, Altitude, Three Incenters, Circumcircles, Incircle, Congruence. |
![Right Triangle, Altitude, Three Incircles, Circumradius](../school-college/p793-right-triangle-altitude-3-incenters-circumradius-distance-1.jpg) |
Geometry Problem 793
Right Triangle, Altitude, Three Incircles, Incenters, Circumcircle, Circumradius, Perpendicular, Distance. |
![Right Triangle, Altitude, Angle Bisector, Three Incircles, Five Concyclic Points, Circles](../school-college/p792-right-triangle-altitude-3-incenters-concyclic-bisector-1.jpg) |
Geometry Problem 792
Right Triangle, Altitude, Angle Bisector, Three Incircles, Five Concyclic Points, Circles. |
![Right Triangle, Altitude, Incenter, Angle Bisector, Inradius](../school-college/p790-right-triangle-altitude-incenter-inradius-congruence-1.jpg) |
Geometry Problem 790
Right Triangle, Altitude, Angle Bisector, Incircle, Tangency Point, Inradius, Circles, Tangent Line, Congruence. |
![Right Triangle, Altitude, Angle Bisector, Inradius](../school-college/p789-right-triangle-altitude-angle-bisector-inradius-1.jpg) |
Geometry Problem 789
Right Triangle, Altitude, Angle Bisector, Incircle, Tangency Point, Inradius, Circles, Tangent Line. |
![Intersecting Circles, Secant Line, Midpoint, Cyclic Quadrilateral](../school-college/p788-intersecting-circle-midpoint-cyclic-quadrilateral-1.jpg) |
Geometry Problem 788
Intersecting Circles, Secant Line, Midpoint, Cyclic Quadrilateral. |
![Right Triangle, Inradius, 18 Equal Circles, Line Tangent, Legs, Hypotenuse, Ratio, Metric Relations](../school-college/p787-right-triangle-circles-tangent-legs-hypotenuse-inradius-1.jpg) |
Geometry Problem 787
Right Triangle, Inradius, 18 Equal Circles, Line Tangent, Legs, Hypotenuse, Ratio, Metric Relations. |
![Triangle, Orthocenter, Circumcircle, Diameter, Midpoint](../school-college/p783-triangle-orthocenter-circumcircle-diameter-midpoint-1.jpg) |
Geometry Problem 783
Triangle, Orthocenter, Circumcenter, Circumcircle, Diameter, Altitude, Midpoint. |
![Triangle, Orthocenter, Circumcircle, Diameter, Altitude, Parallelogram](../school-college/p782-triangle-orthocenter-circumcircle-diameter-parallelogram-1.jpg) |
Geometry Problem 782
Triangle, Orthocenter, Circumcenter, Circumcircle, Diameter, Altitude, Parallelogram. |
![Triangle, Orthocenter, Circumcenter, Vertex, Altitude, Midpoint, Perpendicular](../school-college/p781-triangle-circumcenter-perpendicular-orthocenter-midpoint-1.jpg) |
Geometry Problem 781
Triangle, Orthocenter, Circumcenter, Vertex, Altitude, Midpoint, Perpendicular. |
![Triangle, Orthocenter, Inradius, Circumradius](../problem/p780-triangle-distance-orthocenter-vertex-circumradius-inradius-1.jpg) |
Geometry Problem 780
Triangle, Sum of Inradius and Circumradius, Distances from the Orthocenter to the Vertices. |
![Triangle, Distance from the Orthocenter to a Vertex, Circle, Circumradius, Side, Square.](../problem/p778-triangle-altitude-orthocenter-vertex-circumradius-side-1.jpg) |
Geometry Problem 778
Triangle, Distance from the Orthocenter to a Vertex, Circle, Circumradius, Side, Square. |
![Triangle, Distance from the Orthocenter, Vertex, Circle, Circumradius, Cosine](../problem/p777-triangle-altitude-orthocenter-vertex-circumradius-cosine-1.jpg) |
Geometry Problem 777
Triangle, Distance from the Orthocenter to a Vertex, Circle, Circumradius, Cosine. |
![Triangle, Isogonal lines, Congruent angles, Perpendicular](../problem/p776-triangle-isogonal-perpendicular-feet-concyclic-midpoint-1.jpg) |
Geometry Problem 776
Triangle, Isogonal lines, Congruent angles, Perpendicular, Concyclic points, Circle, Center, Midpoint. |
![Triangle, Two Altitudes, Circumcircle, Tangent, Parallel](../problem/p774-triangle-circumcircle-altitude-tangent-parallel-1.jpg) |
Geometry Problem 774
Triangle, Two Altitudes, Circumcircle, Tangent at a Vertex, Parallel. |
![Intersecting Circles, Midpoint, Secant, Bisection](../problem/p773-intersecting-circles-midpoint-secant-1.jpg) |
Geometry Problem 773
Intersecting Circles, Midpoint, Secant line, Bisection. |
![Triangle, Circumcircle, Circumcenter, Orthocenter, Midpoint arc, Parallel chord, Congruence](../problem/p770-parallelogram-triangle-circumcenter-angle-bisector-1.jpg) |
Geometry Problem 770
Parallelogram, Angle Bisector, Triangle, Circumcenter, Circumcircle, Angle Measurement. |
![Triangle, Circumcircle, Circumcenter, Orthocenter, Midpoint arc, Parallel chord, Congruence](../problem/p769-triangle-circumcenter-orthocenter-midpoint-arc-parallel-congruence-1.jpg) |
Geometry Problem 769
Triangle, Circumcircle, Circumcenter, Orthocenter, Midpoint of arc, Parallel to chord, Congruence. |
![Equilateral triangle, Circle, Tangent](../problem/p767-equilateral-triangle-tangent-to-circle-1.jpg) |
Geometry Problem 767
Equilateral Triangle, Circle tangent to a side, Tangent line, Measurement, Secant. |
![Isosceles Triangle, Circle, Diameter, Altitude, Chord](../problem/p760-isosceles-triangle-circle-diameter-metric-relations-1.jpg) |
Geometry Problem 760
Isosceles Triangle, Circle, Diameter, Altitude, Chord, Metric relations. |
![Four Circles Theorem. TracenPoche](../geometry/four_circles_concyclic_17.jpg) |
Geometry Problem 756: Four Circles Theorem
Using TracenPoche Interactive Dynamic Software.
Step-by-Step construction, Manipulation, and animation. |
![Square, Circle, Angle](../problem/p752-square-circle-angle-1.jpg) |
Geometry Problem
752.
Square, Circle, Tangent, Chord, Angle. |
![Circle, Chord, Congruence, 90 Degrees](../problem/p745-circle-chord-congruence-90-degrees-1.jpg) |
Geometry Problem
745.
Circle, 90 Degrees, Chord, Congruence, Perpendicular, Metric Relations. |
![Parallelogram, Circle, Chord](../problem/p744-parallelogram-circle-diameter-chord-congruence-1.jpg) |
Geometry Problem
744.
Parallelogram, Circle, Diameter, Chord, Congruence, Triangle, Metric Relations. |
![Cyclic quadrilateral, tangent, perpendicular](../problem/p737_cyclic_quadrilateral_1.jpg) |
Geometry Problem
737.
Cyclic Quadrilateral, Circumscribed Circle, Diameter, Tangent, Perpendicular. |
![Triangle, Orthocenter, Circumcircle](../problem/p729_triangle_orthocenter1.jpg) |
Geometry Problem
729.
Triangle, Altitude, Orthocenter, Circumcircle, Perpendicular, Midpoint. |
![Triangle, Circle, Concurrency](../problem/p728_triangle_concurrent_1.jpg) |
Geometry Problem
728.
Triangle, Altitude, Perpendicular, Circumcircle, Midpoint, Intersecting Circles, Concurrency. |
![Circumscribed Quadrilateral, Angles](../problem/p724_quadrilateral_circle1.jpg) |
Geometry Problem
724.
Circumscribed Quadrilateral, Circle, Angle, Incenter, Half
the Measure. |
![Squares, Circles, Collinear](../problem/p723_squares_circles_1.jpg) |
Geometry Problem
723.
Squares, Circumscribed Circles, Collinear points. |
![Squares, CIrcles, Collinear](../problem/p722_squares_circles_1.jpg) |
Geometry Problem
722.
Squares, Circumscribed Circles, Collinear points. |
![Tangent Circles, Incenter, Chord](../problem/p713_tangent_circles_1.jpg) |
Geometry Problem
713.
Tangent Circles, Diameter, Chord, Tangent, Incenter, Incircle, Triangle. |
![Semicircles, Tangent, Perpendicular, Angle](../problem/p712_tangent_circles_1.jpg) |
Geometry Problem
712.
Semicircle, Diameter, Tangent, Perpendicular, Angle Measure. |
![Circle, Area, Tangent, Intersecting, Lune](../problem/p708_circle_area_lune_1.jpg) |
Geometry Problem
708.
Circle, Tangent, Intersecting, Lune, Area, Diameter. |
![Triangle, Excenter, Angle](../problem/p707_excenters_angles_1.jpg) |
Geometry Problem
707.
Triangle, Excenters, Angle Bisectors, Angle, Measurement. |
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Antonio Gutierrez
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