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Right triangle ABC with altitude d

Source: Canadian Repêchage 2009: Problem 2

April 25, 2014

geometryPythagorean Theoremgeometry proposedtrigonometry

Problem Statement

Triangle

ABC

is right-angled at

C

with

AC = b

and

BC = a

. If

d

is the length of the altitude from

C

AB

, prove that

\dfrac{1}{a^2}+\dfrac{1}{b^2}=\dfrac{1}{d^2}