Problem #PRU-5229

Problem

We have a triangle \(\triangle ABC\) with side lengths \(|AB|=3\), \(|AC|=4\) and angle \(\angle BAC=90^{\circ}\). A circle is drawn with side \(BC\) as diameter, and two semicircles are drawn with sides \(AB\) and \(AC\) as diameters. Find the area of the red part.