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Geometry: Incenter, Incircle, Inradius of a triangle, Theorems
and Problems.
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Proposed Problem 439.
Isosceles triangle, Cevian, Incenter, Angles, Circle. |
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Proposed Problem 435.
Triangle, Incircle, Inradius, Incenter, Congruent circles, tangent,
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 378.
Triangle, Incenter, Parallel to a side, Angle, Congruence. |
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Proposed Problem 374.
Triangle, Incenter, Internal Angle Bisectors. |
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Proposed Problem 320.
Triangle, Circumcircle, Incenter, Excenter, Collinear points. |
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Sangaku Geometry Theorem: Cyclic Quadrilateral.
Incenters, Incircles, Inradii, Rectangle. |
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Sangaku Problem (An Old Japanese Theorem).
Incenters, Incircles, Inradii, Carnot's theorem. |
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Equal Incircles Theorem: Triangles,
cevians, circles. |
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Adams' Circle
Theorem
Concentric to the Incircle. |
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Spieker Center
Incenter of the medial triangle. |
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Heron's Formula.
Key facts and
a purely geometric
step-by-step proof.
Incenter, Incircle, Excenter.
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Semiperimeter and incircle of a triangle. |
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Semiperimeter, incircle and excircles of a triangle.
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Gergonne Point Theorem.
Incenter, Incircle, Concurrency. Interactive proof with animation.
Key concept: Ceva's Theorem.
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The Bevan Point The
circumcenter of the excentral triangle.
Illustration with animation.
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Interactive Gergonne Line and Nobbs Points.
Dynamic Geometry.
Step-by-Step construction, Manipulation, and animation.
Incenter and the points of contact of the incircle. |
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Triangle: Incircle, Perpendicular, Angle Bisector.
Dynamic Geometry.
Step-by-Step construction, Manipulation, and animation.
Prove proposition. |
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Right Triangles, Formulas and Facts
Pythagorean theorem, Similarity, Geometric mean,
hypotenuse, cathetus (legs), semiperimeter, altitude, median,
similar shapes areas, centers, orthocenter, incenter,
incircle, centroid, circumcenter, radius, inradius. |
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Feuerbach
Point Facts
Incenter, Incircle, Nine point circle, Circumcircle. |
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Feuerbach
Theorem, Acute Triangle illustration
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Feuerbach
Theorem, Obtuse Triangle illustration
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Feuerbach
Theorem, Right Triangle illustration
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Feuerbach Theorem
One of the most striking theorems in triangle geometry. |
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Proposed Problem 279 Incircle.
Tangent Circles, Common External Tangent, Chords, Inradius. |
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Proposed Problem 275.
Right Triangle, Incenter, Circumcircle, Sagitta, Inradius. |
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Proposed Problem 260.
Equilateral Triangle, Incircle, Tangency Points, Vertices, Distances,
Squares.
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Proposed Problem 259.
Equilateral Triangle, Incircle, Tangency Points, Side, Distances,
Squares.
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Proposed Problem 258 Incircle.
Equilateral Triangle, Circumcircle, Point, Vertices, Side, Distances,
Squares.
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Proposed Problem 248.
Napoleon's Theorem III. Inner and outer Napoleon triangles, Area.
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