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fixed circle, starting with two intersecting circles and an orthocenter

Source: Ukrainian Geometry Olympiad 2017, IX p3, X p2

December 12, 2018

geometryfixedintersectcirclesLocusLocus problems

Problem Statement

Circles

{w}_{1},{w}_{2}

intersect at points

{{A}_{1}}

and

{{A}_{2}}

. Let

B

be an arbitrary point on the circle

{{w}_{1}}

, and line

B{{A}_{2}}

intersects circle

{{w}_{2}}

at point

C

. Let

H

be the orthocenter of

\Delta B{{A}_{1}}C

. Prove that for arbitrary choice of point

B

, the point

H

lies on a certain fixed circle.