MathDB
CE^2/BF^2= AJ x JE / AK x KF

Source: Indonesia INAMO Shortlist 2010 G11

August 27, 2021
geometryperpendicular bisectorratio

Problem Statement

Given triangle ABCABC and point PP on the circumcircle of triangle ABCABC. Suppose the line CPCP intersects line ABAB at point EE and line BPBP intersect line ACAC at point FF. Suppose also the perpendicular bisector of ABAB intersects ACAC at point KK and the perpendicular bisector of ACAC intersects ABAB at point JJ. Prove that (CEBF)2=AJ⋅JEAK⋅KF\left( \frac{CE}{BF}\right)^2= \frac{AJ \cdot JE }{ AK \cdot KF}
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