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1/BC - 2/ DC = 1 / CA if <ACB = 2 < CAB

Source: Mathematics Regional Olympiad of Mexico Center Zone 2007 P5

November 8, 2021

equal anglesgeometry

Problem Statement

Consider a triangle

ABC

with

\angle ACB = 2 \angle CAB

and

\angle ABC> 90 ^ \circ

. Consider the perpendicular on

AC

that passes through

A

and intersects

BC

D

, prove that

\frac {1} {BC} - \frac {2} {DC} = \frac {1} {CA}