MathDB
Cyclic quadrilateral with a side which is diameter

Source: 0

April 23, 2009

Problem Statement

Let ABCD ABCD be convex quadrilateral with \angle C\equal{}\angle D\equal{}90{}^\circ. The circle K K passing through A A and B B is tangent to CD CD at C C. Let E E be the intersection of K K and [AD] \left[AD\right]. If \left|BC\right|\equal{}20, \left|AD\right|\equal{}16, then ∣CE∣ \left|CE\right| is
<spanclass=′latex−bold′>(A)</span> 9<spanclass=′latex−bold′>(B)</span> 62<spanclass=′latex−bold′>(C)</span> 45<spanclass=′latex−bold′>(D)</span> 72<spanclass=′latex−bold′>(E)</span> 10<span class='latex-bold'>(A)</span>\ 9 \qquad<span class='latex-bold'>(B)</span>\ 6\sqrt{2} \qquad<span class='latex-bold'>(C)</span>\ 4\sqrt{5} \qquad<span class='latex-bold'>(D)</span>\ 7\sqrt{2} \qquad<span class='latex-bold'>(E)</span>\ 10
Back to ProblemsView on AoPS