Problem

Source: Ukraine 1999 Grade 10 P2

Tags: geometry, Triangle, Triangles



Let M be a point inside a triangle ABC. The line through M parallel to AC meets AB at N and BC at K. The lines through M parallel to AB and BC meet AC at D and L, respectively. Another line through M intersects the sides AB and BC at P and R respectively such that PM=MR. Given that the area of ABC is S and that CKCB=a, compute the area of PQR.