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P17 [Geometry] - Turkish NMO 1st Round - 2003

Source:

May 15, 2014
geometry

Problem Statement

The circle C1C_1 and the circle C2C_2 passing through the center of C1C_1 intersect each other at AA and BB. The line tangent to C2C_2 at BB meets C1C_1 at BB and DD. If the radius of C1C_1 is 3\sqrt 3 and the radius of C2C_2 is 22, find ∣AB∣∣BD∣\dfrac{|AB|}{|BD|}.
<spanclass=′latex−bold′>(A)</span> 12<spanclass=′latex−bold′>(B)</span> 32<spanclass=′latex−bold′>(C)</span> 232<spanclass=′latex−bold′>(D)</span> 1<spanclass=′latex−bold′>(E)</span> 52 <span class='latex-bold'>(A)</span>\ \dfrac 12 \qquad<span class='latex-bold'>(B)</span>\ \dfrac {\sqrt 3}2 \qquad<span class='latex-bold'>(C)</span>\ \dfrac {2\sqrt 3}2 \qquad<span class='latex-bold'>(D)</span>\ 1 \qquad<span class='latex-bold'>(E)</span>\ \dfrac {\sqrt 5}2
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