MathDB

Inscribed circle (St. Petersburg, 2002)

Source: Bulgarian MO 2007, Day 1, Problem 1

May 16, 2007

geometrytrigonometrygeometric transformationreflectionrhombusinradiuscircumcircle

Problem Statement

The quadrilateral

ABCD

, where

\angle BAD+\angle ADC>\pi

, is inscribed a circle with centre

I

. A line through

I

intersects

AB

and

CD

in points

X

and

Y

respectively such that

IX=IY

. Prove that

AX\cdot DY=BX\cdot CY