JAMB 1991 · UME · Q35

Circle geometry

In the figure, $PMN$ and $PQR$ are two secants of the circle $MQTRN$ and $PT$ is a tangent. If $PM = 5$ cm, $PN = 12$ cm and $PQ = 4.8$ cm, calculate the lengths of $PR$ and $PT$ respectively, in centimetres.

Not to scale: the same figure serves both questions.

Worked solution (try it first)

For secants from $P$ : $PQ \times PR = PM \times PN$ .
Here $PM \times PN = 5 \times 12 = 60$ .
So $4.8 \times PR = 60$ and $PR = 60 \div 4.8 = 12.5$ cm.
For the tangent: $PT^2 = PM \times PN = 60$ , so $PT = \sqrt{60} \approx 7.7$ cm.
In the order asked, $PR$ then $PT$ : 12.5, 7.7, option C.

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