MathDB
AK = KP if H'P_|_ AB

Source: IFYM - XI International Festival of Young Mathematicians Sozopol 2022, Theme for 11-12 grade, 4th round p3

November 12, 2022
equal segmentsgeometry

Problem Statement

Given an acute-angled △AB\vartriangle ABC with altitude AHAH ( ∠BAC>45o>∠AB\angle BAC > 45^o > \angle ABC). The perpendicular bisector of ABAB intersects BCBC at point DD. Let KK be the midpoint of BFBF, where FF is the foot of the perpendicular from CC on ADAD. Point H′H' is the symmetric to HH wrt KK. Point PP lies on the line ADAD, such that H′P⊥ABH'P \perp AB. Prove that AK=KPAK = KP.
Back to ProblemsView on AoPS