Question

If from a external point P of a circle with centre O, two tangents PQ and PRare drawn such that angle of QPR=120. prove tht 2PQ=PO.

Answer 1

Your answer is in attachment






hope this helps you

Answer 2

Join PO, OQ and OR

$\sf{\angle{OPQ}=\angle{OPR}=\frac{1}{2}×120°=60°}$

In ∆OQP,we have

$\sf{\angle{OQP}+\angle{OPQ}+\angle{POQ}=180°}$

$\longrightarrow$$\sf{90°+60°+\angle{POQ}=180°}$

$\longrightarrow$$\sf{\angle{POQ}=30°}$

$\therefore$ $\sf{\frac{PQ}{OP}=sin30°=\frac{1}{2}}$

Hence, 2 PQ = OP.