Problem

Source: RMO 2012

Tags: geometry



Let ABCD be a unit square. Draw a quadrant of a circle with A as centre and B;D as end points of the arc. Similarly, draw a quadrant of a circle with B as centre and A;C as end points of the arc. Inscribe a circle ? touching the arc AC internally, the arc BD internally and also touching the side AB. Find the radius of the circle ?.