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Source: 2022 AMC 10A P13

November 11, 2022
2022 AMC 10A P132022 AMCAMC 10AMC2022 AMC 10aTrianglegeometry

Problem Statement

Let △ABC\triangle ABC be a scalene triangle. Point PP lies on BC‾\overline{BC} so that AP‾\overline{AP} bisects ∠BAC\angle BAC. The line through BB perpendicular to AP‾\overline{AP} intersects the line through AA parallel to BC‾\overline{BC} at point DD. Suppose BP=2BP = 2 and PC=3PC = 3. What is ADAD ?
<spanclass=′latex−bold′>(A)</span>8<spanclass=′latex−bold′>(B)</span>9<spanclass=′latex−bold′>(C)</span>10<spanclass=′latex−bold′>(D)</span>11<spanclass=′latex−bold′>(E)</span>12<span class='latex-bold'>(A) </span>8\qquad<span class='latex-bold'>(B) </span>9\qquad<span class='latex-bold'>(C) </span>10\qquad<span class='latex-bold'>(D) </span>11\qquad<span class='latex-bold'>(E) </span>12
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