MathDB
Isosceles

Source: 2022 AMC 10A P23 / 2022 AMC 12A P20

November 11, 2022
2022 AMC 10a2022 AMC 12AAMC2022 AMCtrapezoidAMC 10AMC 12

Problem Statement

Isosceles trapezoid ABCDABCD has parallel sides AD‾\overline{AD} and BC‾,\overline{BC}, with BC<ADBC < AD and AB=CD.AB = CD. There is a point PP in the plane such that PA=1,PB=2,PC=3,PA=1, PB=2, PC=3, and PD=4.PD=4. What is BCAD?\tfrac{BC}{AD}?
<spanclass=′latex−bold′>(A)</span>14<spanclass=′latex−bold′>(B)</span>13<spanclass=′latex−bold′>(C)</span>12<spanclass=′latex−bold′>(D)</span>23<spanclass=′latex−bold′>(E)</span>34<span class='latex-bold'>(A) </span>\frac{1}{4}\qquad<span class='latex-bold'>(B) </span>\frac{1}{3}\qquad<span class='latex-bold'>(C) </span>\frac{1}{2}\qquad<span class='latex-bold'>(D) </span>\frac{2}{3}\qquad<span class='latex-bold'>(E) </span>\frac{3}{4}
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