MathDB
Turkey NMO 2000 1st Round - P29 (Geometry)

Source:

July 25, 2012
geometrygeometric transformationhomothety

Problem Statement

One of the external common tangent lines of the two externally tangent circles with center O1O_1 and O2O_2 touches the circles at BB and CC, respectively. Let AA be the common point of the circles. The line BABA meets the circle with center O2O_2 at AA and DD. If BA=5|BA|=5 and AD=4|AD|=4, then what is CD|CD|?
<spanclass=latexbold>(A)</span> 20<spanclass=latexbold>(B)</span> 27<spanclass=latexbold>(C)</span> 6<spanclass=latexbold>(D)</span> 152<spanclass=latexbold>(E)</span> 45 <span class='latex-bold'>(A)</span>\ \sqrt{20} \qquad<span class='latex-bold'>(B)</span>\ \sqrt{27} \qquad<span class='latex-bold'>(C)</span>\ 6 \qquad<span class='latex-bold'>(D)</span>\ \frac{15}2 \qquad<span class='latex-bold'>(E)</span>\ 4\sqrt5