# Square and Circle | How to Find the Area of the Circle?

# Find the area of the circle when opposite sides of the square are tangent and chord

One side of a square is the chord of a circle, and the opposite side is the tangent of the same circle. Find the area of the circle if the sides of the square are 8 cm.

From figure ABCD is a square, AD is the tangent of the circle and BC is the chord of the circle. Calculate the area of the circle, if the sides of a square are 8 cm long.

## Solution: Area of the circle

We can draw a bisector to chord BC, then

Here PQ is the diameter of the circle because PQ is the bisector of chord BC

Assume diameter of the circle, **PQ = 2 r**

From figure

**OP **= AB = **8 cm**

**OQ** = PQ *−* OP = **2 r – 8**

**OB** = **OC **= 8/2 = **4 cm**

## Apply intersecting chords theorem in figure

OP × OQ = OB × OC

⇒ 8(2*r −* 8) = 4 × 4

⇒ 16*r −* 64 = 16

⇒ 16*r* = 80

⇒ *r* = 5 cm

Now we got radius of the circle = 5 cm

so Area of the circle = π*r*²

⇒ Area of the circle = π* *× 5²

⇒** Area of the circle = 25π cm²**