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P05 [Geometry] - Turkish NMO 1st Round - 2013

Source:

April 16, 2013
geometry

Problem Statement

Let DD be a point on side [BC][BC] of triangle ABCABC where ∣BC∣=11|BC|=11 and ∣BD∣=8|BD|=8. The circle passing through the points CC and DD touches ABAB at EE. Let PP be a point on the line which is passing through BB and is perpendicular to DEDE. If ∣PE∣=7|PE|=7, then what is ∣DP∣|DP|?
<spanclass=′latex−bold′>(A)</span> 5<spanclass=′latex−bold′>(B)</span> 4<spanclass=′latex−bold′>(C)</span> 3<spanclass=′latex−bold′>(D)</span> 2<spanclass=′latex−bold′>(E)</span> None of above <span class='latex-bold'>(A)</span>\ 5 \qquad<span class='latex-bold'>(B)</span>\ 4 \qquad<span class='latex-bold'>(C)</span>\ 3 \qquad<span class='latex-bold'>(D)</span>\ 2 \qquad<span class='latex-bold'>(E)</span>\ \text{None of above}
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