MathDB

3 feet of altitudes and another point concyclic wanted, cyclic given, AC//DE//BF

Source: 2016 Croatia MO p3

August 3, 2020

Concyclicaltitudescyclic quadrilateralgeometry

Problem Statement

Given a cyclic quadrilateral

ABCD

such that the tangents at points

B

and

D

to its circumcircle

k

intersect at the line

AC

. The points

E

and

F

lie on the circle

k

so that the lines

AC, DE

and

BF

parallel. Let

M

be the intersection of the lines

BE

and

DF

. If

P, Q

and

R

are the feet of the altitides of the triangle

ABC

, prove that the points

P, Q, R

and

M

lie on the same circle

Back to Problems View on AoPS