MathDB

2

Part of 2024 Regional Olympiad of Mexico West

Problems(1)

mexican regional collinearity

Source: 2024 Mathematics Regional Olympiad of Mexico West P2

10/21/2024
Let △ABC\triangle ABC be a triangle and HH its orthocenter. We draw the circumference C1\mathcal{C}_1 that passes through HH and its tangent to BCBC at BB and the circumference C2\mathcal{C}_2 that passes through HH and its tangent to BCBC at CC. If C1\mathcal{C}_1 cuts line ABAB again at XX and C2\mathcal{C}_2 cuts line ACAC again at YY. Prove that X,YX,Y and HH are collinear.
geometrycollinear