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Turkey NMO 2000 1st Round - P19 (Combinatorics)

Source:

July 25, 2012
probabilitygeometryarea of a triangleHeron's formula

Problem Statement

Let PP be an arbitrary point inside △ABC\triangle ABC with sides 3,7,83,7,8. What is the probability that the distance of PP to at least one vertices of the triangle is less than 11?
<spanclass=′latex−bold′>(A)</span> π362<spanclass=′latex−bold′>(B)</span> π363<spanclass=′latex−bold′>(C)</span> π36<spanclass=′latex−bold′>(D)</span> 12<spanclass=′latex−bold′>(E)</span> 34 <span class='latex-bold'>(A)</span>\ \frac{\pi}{36}\sqrt 2 \qquad<span class='latex-bold'>(B)</span>\ \frac{\pi}{36}\sqrt 3 \qquad<span class='latex-bold'>(C)</span>\ \frac{\pi}{36} \qquad<span class='latex-bold'>(D)</span>\ \frac12 \qquad<span class='latex-bold'>(E)</span>\ \frac 34
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