## Book: RS Aggarwal - Mathematics

### Chapter: 12. Circles

#### Subject: Maths - Class 10th

##### Q. No. 53 of Multiple Choice Questions (MCQ)

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53
##### Assertion - and - Reason TypeEach question consists of two statements, namely, Assertion (A) and Reason (R). For selecting the correct answer, use the following code:

Let us consider a circle with center O and radius 12 cm

A tangent PQ is drawn at point P such that PQ = 16 cm

To Find : Length of OQ

Now, OP PQ [Tangent at any point on the circle is perpendicular to the radius through point of contact]

In right - angled POQ,

By Pythagoras Theorem

[i.e. (hypotenuse)2 = (perpendicular)2 + (base)2 ]

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

(OQ2 = (12)2 + (16)2

625 = 144 + 256

(OQ)2 = 400

OQ = 20 cm

So,

Assertion is correct, and Reason is also correct.

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