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area of quad. wanted, starting with intersecting circles

Source: III Soros Olympiad 1996-97 R3 10.5 https://artofproblemsolving.com/community/c2416727_soros_olympiad_in_mathematics

May 31, 2024

geometryareas

Problem Statement

Two circles intersect at two points

A

and

B

. The radii of these circles are equal to

R

and

r

, respectively; the angle between the radii going to the points of intersection is equal to

a

. A chord

KM

of length

b

is taken in a circle of radius

r

. Straight lines

KA

KB

MA

and

MB

intersect the other circle for second time at four points. Find the area of the quadrilateral with vertices at these points.