The length of a tangent from a point A at distance 5 cm from the centre of the circle is 4 cm. Find the radius of the circle

Solution:

Let's draw a tangent from point A to the circle as shown below.

A tangent at any point of a circle is perpendicular to the radius through the point of contact.

Therefore, ∠OTA = 90° and ΔOTA is a right-angled triangle.

By Pythagoras theorem,

OA² = OT² + AT²

5² = OT² + 4²

OT² = 25 - 16

OT² = 9

OT = ± 3

Radius OT cannot be negative.

Hence, the radius is 3 cm.

☛ Check: NCERT Solutions for Class 10 Maths Chapter 10

Video Solution:

The length of a tangent from a point A at distance 5 cm from the centre of the circle is 4 cm. Find the radius of the circle

Maths NCERT Solutions Class 10 Chapter 10 Exercise 10.2 Question 6

Summary:

If the length of a tangent from a point A at distance 5 cm from the center of the circle is 4 cm, then the radius of the circle is 3 cm.

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