MathDB
Tangent circles

Source: MEMO 2022 T6

September 2, 2022
geometry

Problem Statement

Let ABCDABCD be a convex quadrilateral such that AC=BDAC = BD and the sides ABAB and CDCD are not parallel. Let PP be the intersection point of the diagonals ACAC and BDBD. Points EE and FF lie, respectively, on segments BPBP and APAP such that PC=PEPC=PE and PD=PFPD=PF. Prove that the circumcircle of the triangle determined by the lines AB,CD,EFAB, CD, EF is tangent to the circumcircle of the triangle ABPABP.
Back to ProblemsView on AoPS