semicircles on sides of a cyclic quadrilateral with perpendicular diagonals
Source: Lusophon 2012 CPLP P6
August 29, 2018
geometrycyclic quadrilateralperpendiculardiagonals
Problem Statement
A quadrilateral is inscribed in a circle of center . It is known that the diagonals and are perpendicular. On each side we build semicircles, externally, as shown in the figure.
a) Show that the triangles and have the equal areas.
b) If cm and cm, determine the area of the shaded region.