Triangles: Theorems and Problems 6
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![Triangles](../geometry/triangles_index_17.jpg) |
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![Geometry problem 1275](../school-college/3/p1275-equilateral-triangle-projection-measure-1.jpg) |
Geometry Problem 1275.
Equilateral Triangle, Perpendicular, Projection, Metric Relations, Measurement. |
![Geometry problem 1274](../school-college/3/p1274-isosceles-triangle-80-20-80-measurement-1.jpg) |
Geometry Problem 1274.
Isosceles Triangle, 80-20-80 Degrees, Area, Inradius, Circumradius, Angle Bisector, Metric Relations, Measurement. |
![Geometry problem 1273](../school-college/3/p1273-triangle-circle-tangent-midpoint-equal-angle-tutoring-1.jpg) |
Geometry Problem 1273.
Circle, Tangent, Secant, Midpoint, Isogonal Lines, Congruent Angles. |
![Geometry problem 1272](../school-college/3/p1272-isosceles-triangle-altitude-midpoint-angle-1.jpg) |
Geometry Problem 1272.
Isosceles Triangle, Median, Midpoint, Perpendicular, 90 Degrees, Angles, Congruence. |
![Geometry problem 1271](../school-college/3/p1271-triangle-incircle-excircle-concyclic-tutoring-1.jpg) |
Geometry Problem 1271.
Triangle, Incircle, Incenter, Excircle, Excenter, Escribed Circle, Tangency Points, Six Concyclic Points. |
![Geometry problem 1270](../school-college/3/p1270-triangle-excircle-bisector-90-degree-1.jpg) |
Geometry Problem 1270.
Triangle, Excircle, Excenter, Escribed Circle, Tangency Points, Perpendicular, 90 Degrees, Angle Bisector. |
![Geometry problem 1269](../school-college/3/p1269-triangle-incircle-bisector-90-degree-1.jpg) |
Geometry Problem 1269.
Triangle, Incircle, Incenter, Inscribed Circle, Tangency Points, Perpendicular, 90 Degrees, Angle Bisector. |
![Geometry problem 1268](../school-college/3/p1268-triangle-circle-angle-bisector-concyclic-1.jpg) |
Geometry Problem 1268.
Triangle, Exterior Angle Bisector, Circumcircle, Circle, Chord, Parallel, Concyclic Points, Cyclic Quadrilateral. |
![Geometry problem 1267](../school-college/3/p1267-triangle-incircle-excircle-90-degree-parallelogram-1.jpg) |
Geometry Problem 1267.
Triangle, Incircle, Excircle, Circle, Tangency Points, Perpendicular, 90 Degrees, Parallelogram. |
![Geometry problem 1266](../school-college/3/p1266-triangle-excircle-90-degree-bisector-1.jpg) |
Geometry Problem 1266.
Triangle, Excircle, Circle, Tangency Points, Perpendicular, 90 Degrees, Angle Bisector. |
![Geometry problem 1265](../school-college/3/p1265-triangle-incircle-90-degree-bisector-1.jpg) |
Geometry Problem 1265.
Triangle, Incircle, Circle, Tangency Points, Perpendicular, 90 Degrees, Angle Bisector. |
![Geometry problem 1264](../school-college/3/p1264-triangle-exterior-angle-bisector-90-degree-concurrent
-1.jpg) |
Geometry Problem 1264.
Triangle, Exterior Angle Bisector, Circumcircle, Circle, Perpendicular, 90 Degrees, Concurrent Lines. |
![Geometry problem 1263](../school-college/3/p1263-triangle-medians-90-degree-perpendicular-1.jpg) |
Geometry Problem 1263.
Triangle, Medians, 90 Degrees, Perpendicular. |
![Geometry problem 1262](../school-college/3/p1262-isosceles-triangle-altitude-median-90-degree-1.jpg) |
Geometry Problem 1262.
Isosceles Triangle, Altitude, Medians, 90 Degrees, Perpendicular. |
![Geometry problem 1261](../school-college/3/p1261-cyclic-quadrilateral-angles-3-4-5-1.jpg) |
Geometry Problem 1261.
Cyclic Quadrilateral, Circle, Diameter, Midpoint, Measurement. |
![Geometry problem 1260](../school-college/3/p1260-triangle-angle-bisector-90-degree-concurrent-1.jpg) |
Geometry Problem 1260.
Triangle, Internal Angle Bisector, Circumcircle, Circle, Perpendicular, 90 Degrees, Concurrent Lines. |
![Geometry problem 1259](../school-college/3/p1259-triangle-circle-diameter-parallel-1.jpg) |
Geometry Problem 1259.
Triangle, Circumcircle, Circle, Diameter, Parallel Lines. |
![Geometry problem 1257](../school-college/3/p1257-triangle-altitude-90-degree-measurement-1.jpg) |
Geometry Problem 1257.
Triangle, Altitude, Perpendicular, 90 Degree, Measurement. |
![Geometry problem 1256](../school-college/3/p1256-parallelogram-angle-bisector-triangle-1.jpg) |
Geometry Problem 1256.
Parallelogram, Angle Bisector, Measurement. |
![Geometry problem 1255](../school-college/3/p1255-right-triangle-angle-3-4-5-collinear-1.jpg) |
Geometry Problem 1255.
Right Triangle,
Angle, 90 Degrees, Perpendicular, Collinear Points. |
![Geometry problem 1253](../school-college/3/p1253-triangle-orthocenter-90-degree-circles-1.jpg) |
Geometry Problem 1253.
Triangle, Orthocenter, Circle, Circumcircle, Altitude, Perpendicular, 90 Degree, Concurrency. |
![Geometry problem 1252](../school-college/3/p1252-hexagon-triangle-area-orthocenter-circumcircle-mind-map-1.jpg) |
Geometry Problem 1252.
Triangle, Circle, Circumcircle, Altitude, Area, Hexagon, Perpendicular, 90 Degrees. Mind Map. |
![Geometry problem 1251](../school-college/3/p1251-triangle-circle-diameter-90-degrees-1.jpg) |
Geometry Problem 1251.
Triangle, Circle, Diameter, Perpendicular, 90 Degrees. |
![Geometry problem 1249](../school-college/3/p1249-cyclic-quadrilateral-bisector-triangle-area-1.jpg) |
Geometry Problem 1249.
Cyclic Quadrilateral, Circle, Triangle, Circumcircle, Angle Bisector, Parallel Lines, Area. |
![Geometry problem 1248](../school-college/3/p1248-triangle-circle-orthocenter-diameter-parallel-1.jpg) |
Geometry Problem 1248.
Triangle, Circumcircle, Circle, Diameter, Orthocenter, Altitude, Parallel Lines. |
![Geometry problem 1247](../school-college/3/p1247-triangle-circumcircle-perpendicular-orthocenter-1.jpg) |
Geometry Problem 1247.
Triangle, Circumcircle, Orthocenter, Altitude, Perpendicular, Midpoint. |
![Geometry problem 1246](../school-college/3/p1246-orthocenter-midpoint-perpendicular-1.jpg) |
Geometry Problem 1246.
Triangle, Orthocenter, Altitude, Midpoint, Perpendicular. |
![Geometry problem 1240](../school-college/3/p1240-triangle-circle-diameter-perpendicular-1.jpg) |
Geometry Problem 1240
Triangle, Circle, Diameter, Circumcircle, Circumcenter, Perpendicular. Mobile Apps. |
![Geometry problem 1238](../school-college/3/p1238-square-equilateral-triangle-metric-relation-mobile-apps-1.jpg) |
Geometry Problem 1238
Square, Equilateral Triangle, Metric Relations. Mobile Apps. |
![Geometry problem 1237](../school-college/3/p1237-imo-2016-problem-1-triangle-parallel-concurrent-1.jpg) |
Geometry Problem 1237
IMO 2016, Problem 1, Triangle, Congruence, Parallel Lines, Midpoint, Concurrency. |
![Geometry problem 1235](../school-college/3/p1235-triangle-cevian-concurrent-circle-1.jpg) |
Geometry Problem 1235
Triangle, Cevians, Concurrency, Circle, Circumcircle. |
![Geometry problem 1234](../school-college/3/p1234-quadrilateral-60-degrees-cyclic-concyclic-midpoint-1.jpg) |
Geometry Problem 1234
Quadrilateral, 60 Degrees, Midpoint, Congruence, Cyclic Quadrilateral, Concyclic Points. |
![Geometry problem 1233](../school-college/3/p1233-orthic-axis-triangle-euler-line-perpendicular-1.jpg) |
Geometry Problem 1233
Triangle, Euler Line, Orthic Axis, Perpendicular, 90 Degrees, Orthic Triangle. |
![Geometry problem 1232](../school-college/3/p1232-orthic-axis-triangle-altitude-collinear-1.jpg) |
Geometry Problem 1232
Triangle, Altitudes, Orthic Triangle, Collinearity, Orthic Axis. |
![Geometry problem 1231](../school-college/3/p1231-triangle-orthocenter-circumcenter-incenter-bisector-1.jpg) |
Geometry Problem 1231
Triangle, Orthocenter, Incenter, Circumcenter, Angle Bisector, Center, Circle. |
![Geometry problem 1230](../school-college/3/p1230-quadrilateral-equilateral-triangle-metric-relations-1.jpg) |
Geometry Problem 1230
Quadrilateral, 60 Degrees, Congruence, Metric Relations. |
![Geometry problem 1229](../school-college/3/p1229-three-tangent-circles-line-3-4-5-triangle-1.jpg) |
Geometry Problem 1229
Three Tangent Circles, Midpoint, Common Tangent Line, 3-4-5 Right Triangle. |
![Geometry problem 1227](../school-college/3/p1227-triangle-circle-bisector-concyclic-cyclic-1.jpg) |
Geometry Problem 1227
Triangle, Circumcircle, Angle Bisector, Concyclic Points, Cyclic Quadrilateral. |
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