Question

From point Q the length of tangent to circle is 24 cm and the distance Q from the centre is 25 cm then the area of the circle is:

A. 7 pi
B. 14 pi
C. 49 pi
D. None of these
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Answer 1

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Let the point of tangency (The point where the tangent and radius meets in a circle) be P and the centre be O.

According to question:

• Length of PQ = 24 cm
• Length of OQ = 25 cm

We know, the tangent is perpendicular to the radius of the circle at the point of tangency. So, ∆OPQ is a right-angled triangle.

By using Pythagoras theoram,

⇛ OP² + PQ² = OQ²

⇛ OP = √OQ² - PQ²

⇛ OP = √25² - 24²

⇛ OP = √49 cm

⇛ OP = 7 cm

Radius of the circle is 7 cm. Now we can find the area of the circle by using formula,

⇛ Area = πr²

⇛ Area = 7² × π

⇛ Area = 49π

The options are in the form of π, hence the correct answer is Option C. And we are done....