In figure 1, PQ is a chord of a circle with centre O and PT is a tangent. If $∠ Q P T = 60^{\circ}$ , find $∠ P R Q$ .

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Solution

Take any point x on circumference
$∠ P \times R = ∠ Q P T$ (angle in all segment = $60^{\circ}$
$∠ Q O P = 2 ∠ P R Q = 120^{\circ}$
$∠ P R Q = \frac{1}{2} R e f l e x ∠ Q O P = \frac{1}{2} (360 - 120)$
$= 120^{\circ}$

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