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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:
3cm
5 cm
10 cm
12.5 cm
$$\triangle$$ 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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