Question

The distance of a point A from the center of a circle is 25 cm and the length of tangent

to the circle from A is 24 cm. Find the diameter of the circle​

Answer 1

QUESTION:-

The distance of a point A from the center of a circle is 25 cm and the length of tangent to the circle from A is 24 cm. Find the diameter of the circle?

SOLUTION:-

Let AP be a tangent drawn from P to a circle with Centre O such that AP = 24 cm & OB = 25 cm

We know that the tangent at any point of a circle is perpendicular to the radius through the point of contact.

In right angled ∆OAP, OA ⟂ AP,

OP² = OA² + AP²

[By Pythagoras theorem]

25² = OA² + 24²

625 = OA² + 576

OA² = 625 - 576

OA² = 49

OA = √49

OA = 7 cm

Hence, the radius of the Circle is 7 cm.

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