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KB = KC wanted, 2 midpoints, 2 perpendiculars related

Source: Mathematics Regional Olympiad of Mexico Center Zone 2020 P3

November 14, 2021
geometryequal segments

Problem Statement

In an acute triangle ABCABC, an arbitrary point PP is chosen on the altitude AHAH. The points EE and FF are the midpoints of ACAC and ABAB, respectively. The perpendiculars from EE on CPCP and from FF on BPBP intersect at the point KK. Show that KB=KCKB = KC.
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