MathDB

29

Part of 2004 National Olympiad First Round

Problems(1)

P29 [Geometry] - Turkish NMO 1st Round - 2004

Source:

11/12/2013
Let MM be the intersection of the diagonals ACAC and BDBD of cyclic quadrilateral ABCDABCD. If ∣AB∣=5|AB|=5, ∣CD∣=3|CD|=3, and m(AMB^)=60∘m(\widehat{AMB}) = 60^\circ, what is the circumradius of the quadrilateral?
<spanclass=′latex−bold′>(A)</span> 53<spanclass=′latex−bold′>(B)</span> 733<spanclass=′latex−bold′>(C)</span> 6<spanclass=′latex−bold′>(D)</span> 4<spanclass=′latex−bold′>(E)</span> 34 <span class='latex-bold'>(A)</span>\ 5\sqrt 3 \qquad<span class='latex-bold'>(B)</span>\ \dfrac {7\sqrt 3}{3} \qquad<span class='latex-bold'>(C)</span>\ 6 \qquad<span class='latex-bold'>(D)</span>\ 4 \qquad<span class='latex-bold'>(E)</span>\ \sqrt{34}
geometrycircumcircletrapezoidtrigonometrycyclic quadrilateralCyclic QuadrilateralsLaw of cosine