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MCQ

From a point Q, 13 cm away from the centre of a circle, the length of tangent PQ to the circle is 12 cm. The radius of the circle (in cm) is

#### Options

A. 25

B. `sqrt313`

C. 5

D. 1

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#### Solution

The given information can be represented diagrammatically as follows:

Let O be the centre of the circle.

**Given:** PQ = 12 cm and OQ = 13 cm.

**To find:** Radius of the circle

PQ is a tangent drawn from the external point Q to the circle.

∠ OPQ = 90° (Radius is perpendicular to the tangent at the point of contact)

On applying Pythagoras theorem in ΔOPQ, we obtain:

OQ^{2} = OP^{2} + PQ^{2}

∴ OP^{2} = OQ^{2} − PQ^{2}

⇒ OP^{2} = (13 cm)^{2} − (12 cm)^{2}

⇒ OP^{2} = 169cm^{2} − 144 cm^{2}

⇒ OP^{2 }= 25 cm^{2}

⇒ OP = 5 cm

Thus, the radius of circle is 5 cm.

Hence, the correct answer is C

Concept: Tangent to a Circle

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