# Intersecting Triangles

Geometry Level 4

Diagram above shows a circle with center $$D$$, with $$C,E,F$$ be points lying on the circle, and two right triangles $$ACD$$ and $$BCE$$ with their hypotenuse intersect at $$F$$. If we are given $$AC = CD = 10 \text{ cm}$$. What is the area of triangle $$ABF$$ to 4 decimal places.

Details and Assumptions

• You may use the approximation: $$\sqrt 2 = 1.41421356$$
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