Problem 112.
Area of Square and Triangle.
Level: High School, SAT Prep, College

In the figure below, given an square
ABCD of area S, E is the intersection of BD and the semicircle
of diameter AD, and CF is tangent to the semicircle. If S_{1} is
the area of triangle DEF, prove that: .

Geometric Art: Hyperbolic Kaleidoscope of problem 112
using iPad Apps: Equilateral Triangles and Squares