MathDB
(APF) intersect (AQE)

Source: Own. IMO 2022 Malaysian Training Camp 2

March 13, 2022
geometry

Problem Statement

Let ABCABC be a triangle, and let BE,CFBE, CF be the altitudes. Let ℓ\ell be a line passing through AA. Suppose ℓ\ell intersect BEBE at PP, and ℓ\ell intersect CFCF at QQ. Prove that:
i) If ℓ\ell is the AA-median, then circles (APF)(APF) and (AQE)(AQE) are tangent.
ii) If ℓ\ell is the inner AA-angle bisector, suppose (APF)(APF) intersect (AQE)(AQE) again at RR, then ARAR is perpendicular to ℓ\ell.
Back to ProblemsView on AoPS