MathDB
2015 Geometry #10

Source:

July 1, 2022
2015Geometry Test

Problem Statement

Triangle ABCABC has ∠BAC=90∘\angle BAC=90^\circ. A semicircle with diameter XYXY is inscribed inside △ABC\triangle ABC such that it is tangent to a point DD on side BCBC, with XX on ABAB and YY on ACAC. Let OO be the midpoint of XYXY. Given that AB=3AB=3, AC=4AC=4, and AX=94AX=\tfrac{9}{4}, compute the length of AOAO.
Back to ProblemsView on AoPS