MathDB
concurrent wanted, mixtilinear incircle from '99

Source: V Soros Olympiad 1998-99 Round 1 11.10 https://artofproblemsolving.com/community/c2416727_soros_olympiad_in_mathematics

May 25, 2024
geometryconcurrency

Problem Statement

Consider a circle tangent to sides ABAB and ACAC (these sides are not equal) of triangle ABCABC and the circumscribed circle around it. Let KK, MM and PP be the touchpoints of this circle with the sides of the triangle and with the circle circumscribed around it, respectively, and let LL be the midpoint of the arc BCBC (not containing AA). Prove that the lines KMKM, PLPL and BCBC intersect at one point.