The Bevan point of a triangle | plane geometry | intermediate level

2 months ago
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Science mathematics geometry plane geometry classical geometry Euclidean geometry triangle line triangle center Bevan Bevan point

Episode 115.

The Bevan point of a triangle | plane geometry | intermediate level.

Branch of mathematics: plane geometry.
Difficulty level: intermediate.

Theorem 1. Let $ABC$ be a triangle. Let $I_A$, $I_B$, $I_C$ be the centers of the excircles of the triangle $ABC$ and let $T_A'$, $T_B'$, $T_C'$ be the tangency points of those excircles with the sides. Then the lines $I_AT_A'$, $I_BT_B'$, $I_CT_B'$ intersect at a single point (which is called the Bevan point of the triangle $ABC$).

Mathematics. Geometry. Plane geometry.
#Mathematics #Geometry #PlaneGeometry

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