MathDB
Cyclic quadrilateral bisectors

Source: Moldova TST 2014, Second Day, Problem 3

March 30, 2014
geometrycircumcircletrapezoidgeometry proposed

Problem Statement

Let ABCDABCD be a cyclic quadrilateral. The bisectors of angles BADBAD and BCDBCD intersect in point KK such that K∈BDK \in BD. Let MM be the midpoint of BDBD. A line passing through point CC and parallel to ADAD intersects AMAM in point PP. Prove that triangle △DPC\triangle DPC is isosceles.
Back to ProblemsView on AoPS