MathDB
Concurrent lines with midpoint

Source: Turkey JBMO TST 2023 Day 1 P2

April 30, 2023
geometryconcurrency

Problem Statement

Let ABCABC is acute angled triangle and K,LK,L is points on AC,BCAC,BC respectively such that ∠AKB=∠ALB\angle{AKB}=\angle{ALB}. PP is intersection of ALAL and BKBK and QQ is the midpoint of segment KLKL. Let T,ST,S are the intersection AL,BKAL,BK with (ABC)(ABC) respectively. Prove that TK,SL,PQTK,SL,PQ are concurrent.
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