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3 squares on sides of a triangle exterally, difference of areas

Source: TOT 498 1996 Spring S O5 Tournament Of Towns

August 16, 2024
geometrySquaresareas

Problem Statement

The squares ABMNABMN, BCKLBCKL and ACPQACPQ are constructed outside triangle ABCABC. The difference between the areas of ABMNAB MN and BCKLBCKL is dd. Find the difference between the areas of the squares with sides NQNQ and PKPK respectively, if ∠ABC\angle ABC is
(a) a right angle; (b) not necessarily a right angle.
(A Gerko)
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