MathDB

1/QD = 1/QB + 1/QC, inscribed equilateral (2012 UNSW S5 Australia)

Source:

January 1, 2021

geometryEquilateral

Problem Statement

A line drawn from the vertex

A

of the equilateral triangle

ABC

meets the side

BC

D

and the circumcircle of the triangle at point

Q

. Prove that

\frac{1}{QD} = \frac{1}{QB} + \frac{1}{QC}