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Find BAC

Source: Iranian National Olympiad (3rd Round) 2008

September 12, 2008

geometrycircumcirclepower of a pointradical axisgeometry proposed

Problem Statement

Let

ABC

be an isosceles triangle with AB\equal{}AC, and

AN

be midpoint of

BC

, and

E

be foot of altitude from

C

. Let

H

be orthocenter of

ABC

and

N

be midpoint of

CE

.

AN

intersects with circumcircle of triangle

ABC

at

K

. The tangent from

C

to circumcircle of

ABC

intersects with

AD

at

F

. Suppose that radical axis of circumcircles of

CHA

and

CKF

is

BC

. Find

\angle BAC

.

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