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# The Length of a Tangent from a Point A at distance 5 cm from the Centre of the circle is 4cm. Find the radius of the Circle.

Learn to find the radius when the length of a tangent and the center of a circle is known.

by Maivizhi A

**Updated **Mar 15, 2024

## The Length of a Tangent from a Point A at distance 5 cm from the Centre of the circle is 4cm. Find the radius of the Circle.

To solve this problem, AB is a tangent drawn on the above circle from point A.

AB is a tangent drawn on this circle from point A.

Using Pythagoras theorem,

a² + b² = c²

In the above circle,

OA² + OT² = AT²

So, substitute the values

5² + r² = 4²

25 + r² = 16

r² = 25 - 16

r² = 9

r = √9

r = 3

So, the radius of the circle is 3 cm.

## Some Problems For You to Work out

We have given you some problems. Try solving these problems to get a better understanding about Tangents and circles.

1. Find the length of the tangent drawn to a circle of radius 3cm, from a point distnt 5 cm from the center.

2. The Length of a Tangent from a Point A at distance 10 cm from the Centre of the circle is 8 cm. Find the radius of the Circle.

## The Length of a Tangent from a Point A at distance 5 cm from the Centre of the circle is 4cm. Find the radius of the Circle - FAQs

1. What is Pythagoras theorem formula?

a² + b² = c²

2. What do you need to find in the above problem?

We need to find the radius of a circle.

3. What is the given distance for the OA?

The distance for O and A is 5 cm.

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