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Chords in a Circle

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June 13, 2009
geometrycyclic quadrilateral

Problem Statement

In a circle with center O O, chord AB‾ \overline{AB} equals chord AC‾ \overline{AC}. Chord AD‾ \overline{AD} cuts BC‾ \overline{BC} in E E. If AC \equal{} 12 and AE \equal{} 8, then AD AD equals: <spanclass=′latex−bold′>(A)</span> 27<spanclass=′latex−bold′>(B)</span> 24<spanclass=′latex−bold′>(C)</span> 21<spanclass=′latex−bold′>(D)</span> 20<spanclass=′latex−bold′>(E)</span> 18 <span class='latex-bold'>(A)</span>\ 27\qquad <span class='latex-bold'>(B)</span>\ 24\qquad <span class='latex-bold'>(C)</span>\ 21\qquad <span class='latex-bold'>(D)</span>\ 20\qquad <span class='latex-bold'>(E)</span>\ 18
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