MathDB

concyclic wanted, orthocenter and circumcircle related

Source: 2017 Saudi Arabia JBMO Training Tests p7

May 28, 2020

geometrycircumcircleorthocenterConcyclic

Problem Statement

Let

ABC

be a triangle inscribed in the circle

(O)

, with orthocenter

H

. Let d be an arbitrary line which passes through

H

and intersects

(O)

P

and

Q

. Draw diameter

AA'

of circle

(O)

. Lines

A'P

and

A'Q

meet

BC

K

and

L

, respectively. Prove that

O, K, L

and

A'

are concyclic.