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area of non convex quad wanted

Source: V Soros Olympiad 1998-99 Round 3 11.8 https://artofproblemsolving.com/community/c2416727_soros_olympiad_in_mathematics

May 26, 2024

geometry

Problem Statement

Side

BC

of triangle

ABC

is equal to

a

and the opposite angle is equal to

\theta

. A straight line passing through the midpoint of

BC

and the center of the inscribed circle intersects lines

AB

and

AC

at points

M

and

P

, respectively. Find the area of the quadrilateral (non-convex)

BMPC