MathDB
Tangent circles to right triangle

Source: 2021 AMC 12B #22

November 17, 2021
AMCAMC 12AMC 12 Bgeometrycoordinate

Problem Statement

Right triangle ABCABC has side lengths BC=6BC=6, AC=8AC=8, and AB=10AB=10. A circle centered at OO is tangent to line BCBC at BB and passes through AA. A circle centered at PP is tangent to line ACAC at AA and passes through BB. What is OPOP?
<spanclass=latexbold>(A)</span> 238<spanclass=latexbold>(B)</span> 2910<spanclass=latexbold>(C)</span> 3512<spanclass=latexbold>(D)</span> 7325<spanclass=latexbold>(E)</span> 3<span class='latex-bold'>(A)</span> ~\frac{23}{8}\qquad<span class='latex-bold'>(B)</span> ~\frac{29}{10}\qquad<span class='latex-bold'>(C)</span> ~\frac{35}{12}\qquad<span class='latex-bold'>(D)</span> ~\frac{73}{25}\qquad<span class='latex-bold'>(E)</span> ~3