MathDB

balkan "slicing" problem

Source: JBMO 2007, Bulgaria, problem 2

June 28, 2007

trigonometrygeometryincenterfunctioncircumcirclecyclic quadrilateralangle bisector

Problem Statement

Let

ABCD

be a convex quadrilateral with

\angle{DAC}= \angle{BDC}= 36^\circ

\angle{CBD}= 18^\circ

and

\angle{BAC}= 72^\circ

. The diagonals and intersect at point

P

. Determine the measure of

\angle{APD}