MathDB

H not needed

Source: USEMO 2019/1

May 23, 2020

geometrycyclic quadrilateralUSEMOAngle Chasing

Problem Statement

Let

ABCD

be a cyclic quadrilateral. A circle centered at

O

passes through

B

and

D

and meets lines

BA

and

BC

again at points

E

and

F

(distinct from

A,B,C

). Let

H

denote the orthocenter of triangle

DEF.

Prove that if lines

AC,

DO,

EF

are concurrent, then triangle

ABC

and

EHF

are similar.
Robin Son

Back to Problems View on AoPS