Question

In the following figure, PQ is a chord of a circle with centre O and PT is a tangent.If ∠QPT = 60°. Find ∠PRQ​

Answer 1

$\huge\mathbb{SOLUTION:-}$

$\mathsf{M \: \angle OPT \: 90°(Radius \: is \: perpendicular \: to \: the \: tangent)}$

$\mathsf{So, \: \angle OPQ = \angle OPT - \angle QPT}$

$\red{:\implies} \mathsf{90° - 60° = 30°}$

$\mathsf{M \: \angle POQ = 2 \: \angle QPT \: 2 \times 60° = 120°}$

$\mathsf{Reflex \: M \: \angle POQ = 360° - 120° = 240°}$

$\mathsf{M \: \angle PRQ = \frac{1}{2} \: Reflex \: \angle POQ}$

$\red{:\implies} \frac{1}{2} \times 240°$

$\red{:\implies} \mathsf{120°}$

$\therefore \mathsf{PRQ = 120°}$