Westwood's Puzzle

Theorem


Take any rectangle $$ABCD$$ and draw the diagonal $$AC$$.

Inscribe a circle in one of the resulting triangles $$\triangle ABC$$.

Drop perpendiculars $$IEF$$ and $$HEJ$$ from the center of this incircle $$E$$ to the sides of the rectangle.

Then the area of the rectangle $$DHEI$$ equals half the area of the rectangle $$ABCD$$.

Proof
Construct the perpendicular from $$E$$ to $$AC$$, and call it's foot $$G$$.

Call the intersection of $$IE$$ and $$AC$$ $$K$$, and the intersection of $$EH$$ and $$AC$$ $$L$$.



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