2016 AMC 12A Problems/Problem 21
Problem
A quadrilateral is inscribed in a circle of radius Three of the sides of this quadrilateral have length
What is the length of its fourth side?
Solution
Let . Let
be the center of the circle. Then
is twice the altitude of
. Since
is isosceles we can compute its area to be
, hence
.
Now by Ptolemy's Theorem we have .