MathDB
Crazy Coordinate Crisis

Source: 2017 AMC 10B #22 / AMC 12B #18

February 16, 2017
analytic geometryAMCAMC 10geometry2017 AMC 10B2017 AMC 12BAMC 12

Problem Statement

The diameter AB‾\overline{AB} of a circle of radius 22 is extended to a point DD outside the circle so that BD=3BD=3. Point EE is chosen so that ED=5ED=5 and the line EDED is perpendicular to the line ADAD. Segment AE‾\overline{AE} intersects the circle at point CC between AA and EE. What is the area of △ABC\triangle ABC?
<spanclass=′latex−bold′>(A) </span>12037<spanclass=′latex−bold′>(B) </span>14039<spanclass=′latex−bold′>(C) </span>14539<spanclass=′latex−bold′>(D) </span>14037<spanclass=′latex−bold′>(E) </span>12031<span class='latex-bold'>(A) \ </span> \frac{120}{37}\qquad <span class='latex-bold'>(B) \ </span> \frac{140}{39}\qquad <span class='latex-bold'>(C) \ </span> \frac{145}{39}\qquad <span class='latex-bold'>(D) \ </span> \frac{140}{37}\qquad <span class='latex-bold'>(E) \ </span> \frac{120}{31}
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