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Perpendicular Bisectors and Angle Bisectors

Source: AMC 12 A 2002 #23

August 1, 2007
geometrytrigonometryperpendicular bisectortrig identitiesLaw of Sinesangle bisectorarea of a triangle

Problem Statement

In triangle ABC ABC, side AC AC and the perpendicular bisector of BC BC meet in point D D, and BD BD bisects ∠ABC \angle ABC. If AD \equal{} 9 and DC \equal{} 7, what is the area of triangle ABD ABD? <spanclass=′latex−bold′>(A)</span> 14<spanclass=′latex−bold′>(B)</span> 21<spanclass=′latex−bold′>(C)</span> 28<spanclass=′latex−bold′>(D)</span> 145<spanclass=′latex−bold′>(E)</span> 285 <span class='latex-bold'>(A)</span>\ 14 \qquad <span class='latex-bold'>(B)</span>\ 21 \qquad <span class='latex-bold'>(C)</span>\ 28 \qquad <span class='latex-bold'>(D)</span>\ 14\sqrt5 \qquad <span class='latex-bold'>(E)</span>\ 28\sqrt5
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