# 3.   A tangent PQ at a point P of a circle of radius 5 cm meets a line through the centre O at a point Q so that OQ = 12 cm. Length PQ is :       (A) 12 cm       (B) 13 cm       (C) 8.5 cm       (D) $\sqrt { 119}$ cm.

M manish

The correct option is (d) = $\sqrt { 119}$ cm

It is given that the radius of the circle is 5 cm. OQ = 12 cm
According to question,
We know that $\angle QPO=90^0$
So, triangle OPQ is a right angle triangle. By using pythagoras theorem,
$PQ =\sqrt{OQ^2-OP^2}=\sqrt{144-25}$
$=\sqrt{119}$ cm

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