Question

from external point P of a circle with centre O , two tangents PQ and PR are drawn such that angle QPR is 120° , prove that 2PQ = PO​

Answer 1

$\huge\bold{Solution:-}$

From external point P of a circle with centre O , two tangents PQ and PR are drawn such that angle QPR is 120° , prove that 2PQ = PPO.

$\huge\bold{Solution:-}$

Given ∠QPR=120°

Radius is perpendicular to the tangent at the point of contact.

∴∠OQP=90°⇒∠QPO=60°

(tangent drawn to a circle from an external point are equally inclined to the segment, joining the center to that point).

In ΔQPO,cos60°

=

PO

PQ

⇒

2

1

=

PO

PQ

⇒2PQ=PO