Triangles: Theorems and Problems 8
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![Triangles](../geometry/triangles_index_17.jpg) |
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![Geometry Problem 946](../school-college/p946-quadrilateral-diagonal-midpoint-parallel-area-1.jpg) |
Geometry Problem 946.
Triangle, Quadrilateral, Area, Diagonal, Midpoint, Parallel. |
![Geometry Problem 945](../school-college/p945-triangle-concurrent-lines-perpendicular-angle-bisector-1.jpg) |
Geometry Problem 945.
Triangle, Concurrent Lines, Cevians, Perpendicular, Angle Bisector. |
![Geometry Problem 944](../school-college/p944-triangle-orthocenter-altitude-perpendicular-parallel-1.jpg) |
Geometry Problem 944.
Triangle, Orthocenter, Altitude, Perpendicular, 90 Degrees, Parallel Lines. |
![Geometry Problem 943](../school-college/p943-triangle-incircle-parallel-tangency-point-1.jpg) |
Geometry Problem 943.
Triangle, Incircle, Inscribed Circle, Tangency Points, Parallel, Metric Relations. |
![Geometry Problem 942](../school-college/p942-triangle-circumcircle-sagitta-inradius-exradius-1.jpg) |
Geometry Problem 942.
Triangle, Circles, Circumcircle, Sagitta, Incircle, Excircle, Inradius, Exradius, Metric Relations. |
![Problem 939](../school-college/p939-circle-tangent-parallel-secant-midpoint-1.jpg) |
Geometry Problem 939.
Circle, Tangent, Secant, Chord, Parallel, Midpoint. |
![Problem 938](../school-college/p938-cyclic-quadrilateral-circumradius-circumcenter-distance-1.jpg) |
Geometry Problem 938.
Cyclic Quadrilateral, Triangle, Circumcircle, Circles, Circumcenter, Circumradius, Distance, Metric Relations.
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![Problem 937](../school-college/p937-triangle-circle-tangent-circumcircle-midpoint-1.jpg) |
Geometry Problem 937.
Triangle, Circumcircle, Circles, Tangent, Sides, Midpoint.
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![Problem 936](../school-college/p936-semicircle-diameter-circle-tangent-radius-metric-relations-1.jpg) |
Geometry Problem 936.
Circle, Semicircle, Diameter, Tangent, Radius, Chord, Metric Relations.
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![Problem 935](../school-college/p935-equal-incircles-circles-triangle-cevian-1.jpg) |
Geometry Problem 935.
Square, Circle, Center, Perpendicular, Metric Relations.
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![Problem 933](../school-college/p933-square-center-perpendicular-metric-relations-1.jpg) |
Geometry Problem 933.
Square, Center, Transversal, Perpendicular, Metric Relations, Congruence. |
![Problem 932](../school-college/p932-square-midpoint-ratio-3-1-angle-congruence-1.jpg) |
Geometry Problem 932.
Square, Midpoint, Diagonal, Ratio 3:1, Angle Measure, Congruence.
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![Problem 931](../school-college/p931-square-semicircle-circle-angle-metric-relation-1.jpg) |
Geometry Problem 931.
Square, Circle, Semicircle, Diameter, Triangle, Angle, Metric Relations.
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![Problem 930](../school-college/p930-triangle-altitude-circle-diameter-angle-1.jpg) |
Geometry Problem 930.
Acute Triangle, Altitudes, Circles, Diameter, Angle, Measure.
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![Problem 929](../school-college/p929-triangle-orthocenter-reflection-circumcircle-concurrency-1.jpg) |
Geometry Problem 929.
Triangle, Orthocenter, Circumcircle, Reflection, Concurrency.
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![Problem 928](../school-college/p928-triangle-area-median-cevian-concurrency-1.jpg) |
Geometry Problem 928.
Triangle, Midpoint, Median, Cevian, Concurrency, Area.
|
![Problem 927](../school-college/p927-semicircle-equal-arcs-radius-chord-congruence-1.jpg) |
Geometry Problem 927.
Semicircle, Diameter, Radius, Equal Arcs, Chord, Triangle, Congruence.
|
![Problem 926](../school-college/p926-equilateral-triangle-midpoint-perpendicular-metric-relation-1.jpg) |
Geometry Problem 926.
Two Equilateral Triangles, Midpoint, Perpendicular, Metric Relations.
|
![Problem 924](../school-college/p924-quadrilateral-perpendicular-circle-chord-tangent-midpoint-metric-relation-1.jpg) |
Geometry Problem 924.
Quadrilateral, Diagonal, Perpendicular, Circle, Tangent, Midpoint, Metric Relations.
|
![Problem 923](../school-college/p923-infographic-quadrilateral-obtuse-inequality-diagonal-1.jpg) |
Geometry Problem 923.
Quadrilateral, Quadrangle, Obtuse Angle, Triangle, Diagonal, Inequality, Length.
|
![Problem 922](../school-college/p922-circle-tangent-chord-secant-harmonic-mean-1.jpg) |
Geometry Problem 922.
Circle, Tangent Lines, Tangency Points, Chord, Secant, Harmonic Mean.
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![Problem 921](../school-college/p921-right-triangle-circumcircle-midpoint-incircle-1.jpg) |
Geometry Problem 921.
Right Triangle, Circumcircle, Arc, Midpoint, Tangency Point, Incircle.
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![Problem 920](../school-college/p920-triangle-angle-10-20-30-degrees-1.jpg) |
Geometry Problem 920.
Triangle, Angles, 10, 20 Degrees, Congruence.
|
![Problem 919](../school-college/p919-rhombus-perpendicular-parallel-congruence-1.jpg) |
Geometry Problem 919.
Rhombus, Triangle, Perpendicular, 90 Degrees, Congruence.
|
![Problem 918](../school-college/p918-infographic-triangle-incenter-perpendicular-metric-relations-1.jpg) |
Geometry Problem 918.
Triangle, Incenter, Incircle, Angle Bisector, Perpendicular, Metric Relations.
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![Problem 917](../school-college/p917-infographic-triangle-congruence-midpoint-perpendicular-angle-bisector-1.jpg) |
Geometry Problem 917.
Triangle, Congruence, Midpoints, Angle Bisector, Perpendicular.
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![Problem 916](../school-college/p916-infographic-cyclic-quadrilateral-diameter-circle-congruence-1.jpg) |
Geometry Problem 916.
Cyclic Quadrilateral, Three Circles, Diameter, Congruence.
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![Problem 915](../school-college/p915-triangle-circle-cyclic-quadrilateral-concyclic-1.jpg) |
Geometry Problem 915.
Triangle, Intersecting Circles, Concyclic Points, Cyclic Quadrilateral.
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![Problem 914](../school-college/p914-triangle-orthocenter-angle-bisector-parallel-midpoint-1.jpg) |
Geometry Problem 914.
Triangle, Orthocenter, Angle Bisector, Parallel Lines, Midpoint.
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![Problem 913](../school-college/p913-right-triangle-double-triple-angle-metric-relation-1.jpg) |
Geometry Problem 913.
Right Triangle, Double Angle, Triple Angle, Metric Relations.
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![Problem 912](../school-college/p912-right-triangle-double-triple-angle-perpendicular-1.jpg) |
Geometry Problem 912.
Right Triangle, Double Angle, Triple Angle, Perpendicular Lines.
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![Problem 911](../school-college/p911-right-triangle-double-triple-angle-cyclic-quadrilateral-1.jpg) |
Geometry Problem 911.
Right Triangle, Double Angle, Triple Angle, Concyclic Points, Cyclic Quadrilateral.
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![Geometry Problem 902](../school-college/p902-dynamic-triangle-squares-concurrent-ipad-animation-1.jpg) |
Static Diagram of problem 902
Dynamic Geometry Problem
902
Triangle, Four Squares, Center, Concurrent Lines.
GeoGebra, HTML5 Animation for Tablets
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![Geometry Problem 896](../school-college/p896-triangle-orthocenter-midpoint-circle-diameter-collinear-html5-ipad-1.jpg) |
Geometry Problem 896
Triangle, Orthocenter, Midpoint, Median, Intersecting Circles, Diameter, Collinear Points.
GeoGebra, HTML5 Animation for Tablets |
![Geometry Problem 895](../school-college/p895-triangle-incircle-tangent-parallel-collinear-html5-ipad-1.jpg) |
Geometry Problem 895
Triangle, Incircle, Tangency Points, Parallel line, Collinear Points.
GeoGebra, HTML5 Animation for Tablets |
![Geometry Problem 894](../school-college/p894-triangle-incenter-60-degrees-midpoint-parallel-html5-ipad-1.jpg) |
Geometry Problem 894
Triangle, Angle, 60 degrees, Incenter, Midpoint, Parallel Lines.
GeoGebra, HTML5 Animation for Tablets |
![Geometry Problem 893](../school-college/p893-triangle-circumcenter-incenter-circle-collinear-html5-ipad-1.jpg) |
Geometry Problem 893
Triangle, Circumcircle, Incenter, Circle, Tangent, Collinear Points.
GeoGebra, HTML5 Animation for Tablets |
![Geometry Problem 892](../school-college/p892-triangle-60-degrees-orthocenter-circumcenter-html5-ipad-1.jpg) |
Geometry Problem 892
Triangle, 60 degrees, Orthocenter, Circumcenter. |
![Geometry Problem 889](../school-college/p889-carnot-theorem-acute-triangle-inradius-circumradius-html5-ipad-1.jpg) |
Geometry Problem 889
Carnot's Theorem in an acute triangle, Circumcenter,
Circumradius, Inradius. GeoGebra, HTML5 Animation for
Tablets. |
![Problem 887](../school-college/p887-triangle-altitude-bisector-midpoint-concyclic-html5-ipad-1.jpg) |
Geometry Problem 887
Triangle, Altitude, Angle Bisector, Perpendicular, Midpoint,
Concyclic Points. GeoGebra, HTML5 Animation for Tablets. |
![Geometry Problem 882](../school-college/p882-triangle-cevian-congruence-x-2x-7x-angle-1.jpg) |
Geometry Problem 882
Triangle, Angle x, 2x, 7x, Cevian, Congruence, Auxiliary Lines. |
![Geometry Problem 881](../school-college/p881-triangle-three-squares-area-center-1.jpg) |
Geometry Problem 881
Triangle, three Squares, Centers, Areas. |
![Geometry Problem 880](../school-college/p880-triangle-midpoint-perpendicular-hexagon-area-parallelogram-1.jpg) |
Geometry Problem 880
Triangle, Midpoints, Sides, Perpendiculars, Hexagon, Area. |
![Geometry Problem 879](../school-college/p879-square-midpoint-diagonal-ratio-3-1-angle-1.jpg) |
Geometry Problem 879
Square, Midpoint, Diagonal, Ratio 3:1, Angle Measure. |
![Geometry Problem 877](../school-college/p878-square-inscribed-circle-quadrant-metric-relation-1.jpg) |
Geometry Problem 878
Square, Inscribed Circle, Quadrant, Center, Perpendicular, Metric
Relations. |
![Geometry Problem 877](../school-college/p877-square-transversal-similarity-metric-relation-1.jpg) |
Geometry Problem 877
Square, Right Triangle, Similarity, Metric Relations, Transversal. |
![Geometry Problem 876](../school-college/p876-equilateral-triangle-perpendicular-equal-area-1.jpg) |
Geometry Problem 876
Equilateral Triangle, any Point, Perpendicular, Right Triangle Area, Sum
of Areas. |
![Geometry Problem 875](../school-college/p875-triangle-congruent-circles-triple-angle-1.jpg) |
Geometry Problem 875
Congruent Circles, Intersecting Circles, Secant, Center, Angle
Trisection, Triple Angle. |
![Geometry Problem 874](../school-college/p874-isosceles-triangle-cevian-equal-circumcircles-1.jpg) |
Geometry Problem 874
Isosceles Triangle, Circumcircle, Circumcenter, Congruence. |
![Geometry Problem 873: Quadrilateral, Diagonal, Triangle, Angle Bisector, Congruence](../school-college/p873-quadrilateral-diagonal-angle-bisector-triangle-1.jpg) |
Geometry Problem 873
Quadrilateral, Diagonal, Triangle, Angle Bisector, Congruence. |
![Geometry Problem 872: Quadrilateral, Triangle, Angle, 30, 90 degrees](../school-college/p872-angle-30-degrees-triangle-quadrilateral-1.jpg) |
Geometry Problem 872
Quadrilateral, Triangle, Angle, 30, 90 degrees. |
![Geometry Problem 870: Triangle, Median, Three Squares, Centers, Vertices, Collinear Points, Midpoint](../school-college/p870-triangle-median-three-square-collinear-midpoint-1.jpg) |
Geometry Problem 870
Triangle, Median, Three Squares, Centers, Vertices, Collinear Points,
Midpoint. |
![Geometry Problem 869: Triangle, Median, Three Equilateral Triangles, Collinear Points, Midpoint](../school-college/p869-triangle-median-equilateral-collinear-midpoint-1.jpg) |
Geometry Problem 869
Triangle, Median, Three Equilateral Triangles, Collinear Points,
Midpoint. |
![Geometry problem 867, Isosceles Triangle, Median, Perpendicular, Angle, Congruence](../school-college/p867-triangle-isosceles-angles-congruence-1.jpg) |
Geometry Problem 867
Isosceles Triangle, Median, Perpendicular, Angle, Congruence. |
![Geometry problem 865, Parallelogram, Midpoint, Parallel](../school-college/p865-parallelogram-similarity-midpoint-parallel-1.jpg) |
Geometry Problem 865
Parallelogram, Diagonal, Midpoint, Side, Triangle, Parallel, Similarity. |
![Geometry problem 854 about Parallelogram](../school-college/p864-parallelogram-congruence-similarity-metric-relations-1.jpg) |
Geometry Problem 864
Parallelogram, Diagonal, Congruence, Similarity, Metric Relations. |
![Circumscribed trapezoid, Inscribed Circle, Tangent](../school-college/p863-circumscribed-trapezoid-circle-tangent-metric-relations-1.jpg) |
Geometry Problem 863
Circumscribed trapezoid, Inscribed Circle, Tangent, Metric Relations. |
![Trapezoid, Parallel, Equal Areas, RMS, Root Mean Square](../school-college/p862-trapezoid-parallel-equal-areas-rms-1.jpg) |
Geometry Problem 862:
Trapezoid, Parallel, Equal Areas, RMS, Root Mean Square
. |
![Triangle, Incircle, Parallel, Tangent, Metric Relations](../school-college/p861-triangle-incircle-parallel-tangent-metric-relations-1.jpg) |
Geometry Problem 861
Triangle, Incircle, Parallel, Tangent, Metric Relations. |
![Triangle, Three Medians, Parallel, Parallelogram, Area, Congruence](../school-college/p860-triangle-three-medians-area-1.jpg) |
Geometry Problem 860
Triangle, Three Medians, Parallel, Parallelogram, Area, Congruence. |
![Isosceles Right Triangle, Angles,18, 45 Degrees, Congruence, Perpendicular bisector](../school-college/p859-triangle-angle-45-18-degrees-congruence-1.jpg) |
Geometry Problem 859
Isosceles Right Triangle, Angles,18, 45 Degrees, Congruence,
Perpendicular bisector. |
![Isosceles Right Triangle, Cevian, Ratio 2:1, 45 Degrees, Congruence, Angles, Auxiliary Lines](../school-college/p858-isosceles-right-triangle-angle-1.jpg) |
Geometry Problem 858
Isosceles Right Triangle, Cevian, Ratio 2:1, 45 Degrees, Congruence,
Angles, Auxiliary Lines. |
![Problem 856: Triangle, Median, Midpoint, Angles, 30, 45 Degrees, Congruence, Auxiliary Lines](../school-college/p857-triangle-median-midpoint-angle-30-degrees-1.jpg) |
Geometry Problem 857
Triangle, Median, Midpoint, Angles, 30, 45 Degrees, Congruence,
Auxiliary Lines. |
![Problem 856: Quadrilateral, Diagonals, Triangle, Angles, 30 degrees, Congruence, Auxiliary lines](../school-college/p856-quadrilateral-triangle-angle-30-degrees-diagonal-1.jpg) |
Geometry Problem 856
Quadrilateral, Diagonals, Triangle, Angles, 30 degrees, Congruence,
Auxiliary lines. |
![Problem 855: Quadrilateral, Triangle, Angles, 30 degrees, Congruence, Auxiliary lines](../school-college/p855-triangle-angle-30-degrees-auxiliary-lines-1.jpg) |
Geometry Problem 855
Quadrilateral, Triangle, Angles, 30 degrees, Congruence, Auxiliary
lines. |
![Problem 854: Triangle, Parallel lines, Parallelogram, Areas, Similarity, Concurrent lines](../school-college/p854-triangle-parallelogram-parallel-area-similarity-1.jpg) |
Geometry Problem 854
Triangle, Parallel lines, Parallelogram, Areas, Similarity, Concurrent
lines. |
![Problem 853: Square, Arc, Quadrant, Triangle, Perpendicular, Metric Relations](../school-college/p853-square-arc-perpendicular-circle-midpoint-metric-relations-1.jpg) |
Geometry Problem 853
Online Geometry Problem 853: Square, Arc, Quadrant, Triangle,
Perpendicular, Metric Relations. |
![Problem 852: Triangle, Incircle, Inradius, Tangent, Metric Relations](../school-college/p852-triangle-incircle-inradius-tangent-metric-relations-1.jpg) |
Geometry Problem 852
Online Geometry Problem 852: Triangle, Incircle, Inradius, Tangent,
Metric Relations. |
![Problem 851: Triangle, Triple side, Angles, 90 Degrees. Special Right triangle](../school-college/p851-triangle-triple-side-angle-90-degrees-1.jpg) |
Geometry Problem 851
Triangle, Triple side, Angles, 90 Degrees, Special Right triangle, Sides
ratio 1:3. |
![Problem 850: Triangle, Double side, Angles, 90 Degrees. Special Right triangle](../school-college/p850-triangle-double-side-angle-90-degrees-1.jpg) |
Geometry Problem 850
Triangle, Double side, Angles, 90 Degrees. Special Right triangle. |
![Special Right triangle, Catheti or legs ratio 1:3, 18.5 Degrees. Double angle](../school-college/p849-special-right-triangle-catheti-ratio-1-3-angle-18.5-degrees-1.jpg) |
Geometry Problem 849
Special Right triangle, Catheti or legs ratio 1:3, 18.5 Degrees. Double
angle. |
![Special Right triangle, Catheti or legs ratio 1:2, 26.5 Degrees. Double angle](../school-college/p848-special-right-triangle-cathetus-1-2-angle-26.5-degrees-1.jpg) |
Geometry Problem 848
Special Right triangle, Catheti or legs ratio 1:2, 26.5 Degrees. Double
angle. |
![van Lamoen Circle, Triangle, Medians, Centroid, Six Circumcenters, Concyclic Points](../school-college/p847-triangle-centroid-six-circumcenter-concyclic-points-lamoen-1.jpg) |
Geometry Problem 847
van Lamoen Circle, Triangle, Medians, Centroid, Six Circumcenters,
Concyclic Points. |
![Triangle, Medians, Centroid, Four Circumcenters, Concyclic Points, Cyclic Quadrilateral, Similarity](../school-college/p846-triangle-centroid-four-circumcenter-concyclic-points-1.jpg) |
Geometry Problem 846
Triangle, Medians, Centroid, Four Circumcenters, Concyclic Points,
Cyclic Quadrilateral, Similarity. |
![Triangle, Medians, Centroid, Four Circumcenters, Perpendicular, Congruence, Similarity](../school-college/p845-triangle-centroid-four-circumcenter-perpendicular-median-similarity-1.jpg) |
Geometry Problem 845
Triangle, Medians, Centroid, Four Circumcenters,
Perpendicular, Congruence, Similarity. |
![Triangle, Medians, Centroid, Four Circumcenters, Perpendicular, Congruence, Similarity](../school-college/p844-triangle-centroid-four-circumcenter-perpendicular-median-similarity-1.jpg) |
Geometry Problem 844
Triangle, Medians, Centroid, Four Circumcenters,
Perpendicular, Congruence, Similarity. |
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