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2011 Spring LMT Individual Round Problem 20

Source:

September 11, 2023
geometry

Problem Statement

In the figure below, circle OO has two tangents, AC‾\overline{AC} and BC‾\overline{BC}. EF‾\overline{EF} is drawn tangent to circle OO such that EE is on AC‾\overline{AC}, FF is on BC‾\overline{BC}, and EF‾⊥FC‾\overline{EF} \perp \overline{FC}. Given that the diameter of circle OO has length 1010 and that CO=13CO = 13, what is the area of triangle EFCEFC? https://cdn.artofproblemsolving.com/attachments/b/d/4a1bc818a5e138ae61f1f3d68f6ee5adc1ed6f.png
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