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Turkey Junior Olympiad 2000, Part II - P1

Source:

January 18, 2013
geometryangle bisector

Problem Statement

Let ABCABC be a triangle with ∠BAC=90∘\angle BAC = 90^\circ. Construct the square BDECBDEC such as AA and the square are at opposite sides of BCBC. Let the angle bisector of ∠BAC\angle BAC cut the sides [BC][BC] and [DE][DE] at FF and GG, respectively. If ∣AB∣=24|AB|=24 and ∣AC∣=10|AC|=10, calculate the area of quadrilateral BDGFBDGF.
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