MathDB
This screams Stewart

Source: 2019 AMC 10B #16

February 14, 2019
AMCAMC 102019 AMC 10BTrianglesgeometry

Problem Statement

In △ABC\triangle ABC with a right angle at C,C, point DD lies in the interior of AB‾\overline{AB} and point EE lies in the interior of BC‾\overline{BC} so that AC=CD,AC=CD, DE=EB,DE=EB, and the ratio AC:DE=4:3.AC:DE=4:3. What is the ratio AD:DB?AD:DB?
<spanclass=′latex−bold′>(A)</span>2:3<spanclass=′latex−bold′>(B)</span>2:5<spanclass=′latex−bold′>(C)</span>1:1<spanclass=′latex−bold′>(D)</span>3:5<spanclass=′latex−bold′>(E)</span>3:2<span class='latex-bold'>(A) </span> 2:3 \qquad<span class='latex-bold'>(B) </span> 2:\sqrt{5} \qquad<span class='latex-bold'>(C) </span> 1:1 \qquad<span class='latex-bold'>(D) </span> 3:\sqrt{5} \qquad<span class='latex-bold'>(E) </span> 3:2
Back to ProblemsView on AoPS