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find ratio so segments are perpendicular inside equilateral

Source: Czech and Slovak Match 1997 P1

October 1, 2017

ratioEquilateral Triangleperpendiculargeometry

Problem Statement

Points

K

and

L

are chosen on the sides

AB

and

AC

of an equilateral triangle

ABC

such that

BK = AL

. Segments

BL

and

CK

intersect at

P

. Determine the ratio

\frac{AK}{KB}

for which the segments

AP

and

CK

are perpendicular.