MathDB
Right triangle geo with tangents

Source: MEMO 2022 T5

September 2, 2022
geometry

Problem Statement

Let Ω\Omega be the circumcircle of a triangle ABCABC with ∠CAB=90\angle CAB = 90. The medians through BB and CC meet Ω\Omega again at DD and EE, respectively. The tangent to Ω\Omega at DD intersects the line ACAC at XX and the tangent to Ω\Omega at EE intersects the line ABAB at YY . Prove that the line XYXY is tangent to Ω\Omega.
Back to ProblemsView on AoPS