Question 71

From an external point P, a tangent PQ is drawn to a circle, with the centre O, touching the circle at Q. If the distance of P from the centre is 13 cm and length of the tangent PQ is 12 cm, then the radius of the circle is:

Solution

$$\triangle$$ OPQ is a right angle triangle because $$\angle Q = 90\degree$$,

By Pythagoras,

$$(OQ)^2 + (PQ)^2 = (OP)^2$$

$$(OQ)^2 = (13)^2 - (12)^2$$

$$(OQ)^2 = 169 - 144$$

$$(OQ)^2 = 25$$

$$OQ = 5$$

$$\therefore$$ The radius of the circle is 5 cm.

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