TP and TQ are tangents to a circle centre 0, and r is a point on the circumference of the circle as shown in the figure. If angle PTQ = 45º, what is the magnitude of the angle PRO?
\(\overline{PT}\) = \(\overline{PQ}\) ⇒ tangents from an external point are equal
\(T\hat{P}Q\) = \(T\hat{Q}P\) ⇒ base <s of isosceles \(\triangle\) PQT
\(T\hat{P}Q\) = \(\frac{180 - 45}{2}\) = 67\(\frac{1}{2}\)
But \(P\hat{R}Q\) = \(T\hat{P}Q\) = 67\(\frac{1}{2}\) ⇒ <s in alternate segment.
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