Question

the length of a tangent from a point A distance 5 cm from the centre of the circle is 4 cm find the radius of the circle​

Answer 1

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.

Given: Let the circle be with centre O

AB is the tangent from point A

Length of tangent = AB = 4cm

Also, distance of point from circle = 5 cm

Hence OA = 5cm

To find: Radius i.e. OB

Solution:

Since AB is tangent

Hence OB LAB

2 OBA = 90°

(Tangent at any point of circle is perpendicular to the radius through point of contact)

So, A OAB is a right triangle

In right triangle OAB

Using Pythagoras theorem

(Hypotenuse)² = (Height)² + (Base)²

OA² OB²+ AB²

5² = OB² +4²

OB²= 25-16

OB² = 9

OB=√9

OB = √3²

OB = 3

Hence, radius of the circle = OB = 3cm

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