A tangent is drawn at a point P on a circle. A line through the centre O of a ci

Question

A tangent is drawn at a point P on a circle. A line through the centre O of a circle of radius 7 cm cuts the tangent at Q such that PQ = 24 cm. Find OQ.

Options:

A . 10 cm

B . 15 cm

C . 20 cm

D . 25 cm

Answer: Option D
:
D
Since tangent at a point on the circle is perpendicular to the radius throughthatpoint of contact.

A Tangent Is Drawn At A Point P On A Circle. A Line Through ...

∴ O P ⊥ O Q

Inrightangledtriangle OPQ,

{O Q}^{2} = {O P}^{2} + {P Q}^{2} (ByPythagorastheorem)

{O Q}^{2} = 7^{2} + 24^{2}

{O Q}^{2} = 49 + 576

{O Q}^{2} = 625

O Q = \sqrt{625} = 25 c m

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