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 = 2r
OP = AB = 8 cm
OQ = PQ − OP = 2r – 8
OB = OC = 8/2 = 4 cm
Apply intersecting chords theorem in figure
OP × OQ = OB × OC
⇒ 8(2r − 8) = 4 × 4
⇒ 16r − 64 = 16
⇒ 16r = 80
⇒ r = 5 cm
Now we got radius of the circle = 5 cm
so Area of the circle = πr²
⇒ Area of the circle = π × 5²
⇒ Area of the circle = 25π cm²