A triangle is inscribed in a circle of radius and centre

MATHEMATICS · Subjective · IB Diploma Programme · Mathematics: Analysis and Approaches · Geometry and Trigonometry · Geometry and Trigonometry

Problem

A triangle

ABC

is inscribed in a circle of radius

1

and centre

O

. The lines

AO

BO

, and

CO

meet the opposite sides at

D

E

, and

F

, respectively. Then

\frac{1}{AD}+\frac{1}{BE}+\frac{1}{CF}

is equal to _____.