Ceva’s Theorem

Ceva’s theorem (named after an Italian mathematician Giovanni Ceva) is a theorem about triangles in plane geometry. Given a triangle ABC, let the lines AK, BK, and CK be drawn from the vertices to a common point K (not on one of the sides of ABC), to meet opposite sides at P, Q, and R respectively. (The segments AP, BQ, and CR are known as Cevians.) Then, using signed lengths of segments, (AP/RB) x (BP/PC) x (CQ/QA) = 1.

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