MathDB
Turkey NMO 2000 1st Round - P13 (Geometry)

Source:

July 25, 2012
geometrytrigonometryPythagorean Theorem

Problem Statement

Let dd be one of the common tangent lines of externally tangent circles k1k_1 and k2k_2. dd touches k1k_1 at AA. Let [AB][AB] be a diameter of k1k_1. The tangent from BB to k2k_2 touches k2k_2 at CC. If ∣AB∣=8|AB|=8 and the diameter of k2k_2 is 77, then what is ∣BC∣|BC|?
<spanclass=′latex−bold′>(A)</span> 7<spanclass=′latex−bold′>(B)</span> 62<spanclass=′latex−bold′>(C)</span> 10<spanclass=′latex−bold′>(D)</span> 8<spanclass=′latex−bold′>(E)</span> 53 <span class='latex-bold'>(A)</span>\ 7 \qquad<span class='latex-bold'>(B)</span>\ 6\sqrt 2 \qquad<span class='latex-bold'>(C)</span>\ 10 \qquad<span class='latex-bold'>(D)</span>\ 8 \qquad<span class='latex-bold'>(E)</span>\ 5\sqrt 3
Back to ProblemsView on AoPS