2013 AMC 10B Problems/Problem 23
Problem
In triangle , , , and . Distinct points , , and lie on segments , , and , respectively, such that , , and . The length of segment can be written as , where and are relatively prime positive integers. What is ?
Solution
Since , quadrilateral is cyclic. It follows that . In addition, since , triangles and are similar. It follows that . By Ptolemy, we have . Cancelling , the rest is easy. We obtain $DF=\frac{16}{5}\implies{16+5=21}\implies{\boxed{\textbf{(B)} 21}$ (Error compiling LaTeX. Unknown error_msg)