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Possible values of gamma when two areas are equal

Source: Bundeswettbewerb Mathematik 2023, Round 2 - Problem 3

September 8, 2023

geometrygeometry proposedanglesarea of a triangle

Problem Statement

Let

ABC

be a triangle with incenter

I

. Let

M_b

and

M_a

be the midpoints of

AC

and

BC

, respectively. Let

B'

be the point of intersection of lines

M_bI

and

BC

, and let

A'

be the point of intersection of lines

M_aI

and

AC

.
If triangles

ABC

and

A'B'C

have the same area, what are the possible values of

\angle ACB