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Geometry Mathley 4.1 P(1, 2)P(3, 4) = P(1, 4)P(2, 3) = P(1, 3)P(2, 4)

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June 7, 2020

distancecirclegeometry

Problem Statement

Five points

K_i, i = 1, 2, 3, 4

and

P

are chosen arbitrarily on the same circle. Denote by

P(i, j)

the distance from

P

to the line passing through

K_i

and

K_j

. Prove that

P(1, 2)P(3, 4) = P(1, 4)P(2, 3) = P(1, 3)P(2, 4)

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