MathDB
Cyclic quadrilateral

Source: 0

April 28, 2009
geometrycircumcircle

Problem Statement

P P is the intersection point of diagonals of cyclic ABCD ABCD. The circumcenters of △APB \triangle APB and △CPD \triangle CPD lie on circumcircle of ABCD ABCD. If AC \plus{} BD \equal{} 18, then area of ABCD ABCD is ?
<spanclass=′latex−bold′>(A)</span> 36<spanclass=′latex−bold′>(B)</span> 812<spanclass=′latex−bold′>(C)</span> 3632<spanclass=′latex−bold′>(D)</span> 8134<spanclass=′latex−bold′>(E)</span> None<span class='latex-bold'>(A)</span>\ 36 \qquad<span class='latex-bold'>(B)</span>\ \frac {81}{2} \qquad<span class='latex-bold'>(C)</span>\ \frac {36\sqrt 3}{2} \qquad<span class='latex-bold'>(D)</span>\ \frac {81\sqrt 3}{4} \qquad<span class='latex-bold'>(E)</span>\ \text{None}
Back to ProblemsView on AoPS