Geometry Problem 1292

Elements: Square, Circle, Right Triangle, Arc, Inradius, Radius, Incircle, Measurement

The figure below shows a square ABCD inscribed in a circle of center Q and a right triangle AED (angle AED = 90 degrees) with inradius r. If r₁ is the radius of a circle tangent to AE, ED, and arc AD, prove that r₁ = r.sqrt(2).

 

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