A point P is 52 cm away from the centre O of a circle of radius 20 cm. A tangent from P touches the circle at T. What is the length of PT?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 48 cm
The tangent at any point of a circle is perpendicular to the radius through that point, so \(\angle OTP=90^\circ\) and Pythagoras’ theorem applies in \(\triangle OTP\), with OP as the hypotenuse.
OT \(=20\) cm (radius), OP \(=52\) cm
\(PT^2=OP^2-OT^2=52^2-20^2=2704-400=2304\)
\(PT=\sqrt{2304}=48\) cm
