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distinct points

Source:

July 7, 2013
trigonometry

Problem Statement

The three distinct pointsB,C,D B, C, D are collinear with C between B and D. Another point A not on the line BD is such that ∣AB∣=∣AC∣=∣CD∣.|AB| = |AC| = |CD|. Prove that ∠BAC=36BAC = 36 if and only if 1/∣CD∣−1/∣BD∣=1/(∣CD∣+∣BD∣)1/|CD|-1/|BD|=1/(|CD| + |BD|) .
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