The Gergonne 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 intersection cevian Ceva

Episode 95.

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

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

Theorem. Let $ABC$ be a triangle and let $T_A$, $T_B$, $T_C$ be the tangency points of its incircle with the sides $BC$, $CA$, $AB$ respectively. Then the lines $AT_A$, $BT_B$, $CT_C$ intersect at a single point (which is called the Gergonne point of the triangle $ABC$).

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

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