MathDB

Three circles

Source: Sharygin Geometry Olympiad Correspondence Round 2017 P-14 (Grade-9-11)

May 1, 2017

geometry

Problem Statement

Let points

B

and

C

lie on the circle with diameter

AD

and center

O

on the same side of

AD

. The circumcircles of triangles

ABO

and

CDO

meet

BC

at points

F

and

E

respectively. Prove that

R^2 = AF.DE

, where

R

is the radius of the given circle. Proposed by N.Moskvitin