Right Isosceles

Geometry Level 4

Given an isosceles right triangle ABCABC, such that:

AB=AC=1,BAC=π2{AB=AC=1, \quad \angle BAC = \dfrac{\pi}2}

Let DD be a point inside the triangle such that:

ADB=π2,ABD=BCD{\angle ADB = \dfrac{\pi}2, \quad \angle ABD = \angle BCD}

Find the area of ABD\triangle ABD.

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