Question

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

Answer 1

Answer:

Radius of circle is 3cm

Step-by-step explanation:

Given,

• Let AB is length of tangent = 4cm

• Let OA be the distance of the point from circle = 5cm

Now, we have to find the radius of the circle.

Since,

The tangent makes the right angle with the circle.

Therefore, using the pythogoras theorem-

(Hypotenus)² = (Base)² + (Height)²

where,

• Hypotenus = 5cm

• Base = 4cm

• Height = radius

Now,

5² = 4² + (radius)²

25 = 16 + (radius)²

25 - 16 = (radius)²

(radius)² = 9

radius = 3cm