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ﬁnd $\angle {BAC}$

Source: 12-th Hungary-Israel Mathematical Competition 2001

April 16, 2007

geometryincentercircumcircleangle bisectorgeometry proposed

Problem Statement

In a triangle

ABC

B_{1}

and

C_{1}

are the midpoints of

AC

and

AB

respectively, and

I

is the incenter. The lines

B_{1}I

and

C_{1}I

meet

AB

and

AC

respectively at

C_{2}

and

B_{2}

. If the areas of

\Delta ABC

and

\Delta AB_{2}C_{2}

are equal, ﬁnd

\angle{BAC}