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Circle Tangent to Triangle

Source: 2021 Fall AMC 10A #15

November 11, 2021
AMC 10AMCAMC 10 A

Problem Statement

Isosceles triangle ABCABC has AB=AC=36AB = AC = 3\sqrt6, and a circle with radius 525\sqrt2 is tangent to line ABAB at BB and to line ACAC at CC. What is the area of the circle that passes through vertices AA, BB, and C?C? <spanclass=′latex−bold′>(A)</span>24π<spanclass=′latex−bold′>(B)</span>25π<spanclass=′latex−bold′>(C)</span>26π<spanclass=′latex−bold′>(D)</span>27π<spanclass=′latex−bold′>(E)</span>28π<span class='latex-bold'>(A) </span>24\pi\qquad<span class='latex-bold'>(B) </span>25\pi\qquad<span class='latex-bold'>(C) </span>26\pi\qquad<span class='latex-bold'>(D) </span>27\pi\qquad<span class='latex-bold'>(E) </span>28\pi
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