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Orthocenter

Source: St Petersburg Olympiad 2009, Grade 9, P4

August 30, 2017

geometrycircumcircleincenter

Problem Statement

Points

A_1

and

C_1

are on

BC

and

AB

of acute-angled triangle

ABC

.

AA_1

and

CC_1

intersect in

K

. Circumcircles of

AA_1B,CC_1B

intersect in

P

- incenter of

AKC

. Prove, that

P

- orthocenter of

ABC

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