Question

Q.11. P is a centre of the circle, AB is the diameter and C is any point on the circle. BC - 6 ;AC = 8. Find the radius of the circle.​

Answer 1

Given:

AB is the diameter =d of a circle.

ΔABC has the diameter AB as base & the point C is on the circumference.

AC=6 cm and BC=8 cm.

To find out:

Area of shaded portion in the given circle.

Solution:

∠ACB=90

o

since ΔABC has been inscribed in a semicircle.

∴ΔABC is a right one with AB as hypotenuse ..

(i)

So, applying Pythagoras theorem, we have

AB= (AC) 2 +(BC) 2

= (6) 2 +(8) 2

cm=10 cm=d.

∴ The radius of the given circle = 2d = 210

cm=5 cm.

i.e The Area of circle =πr 2

=3.14×5 2 cm 2

=78.5cm 2

.

Again, Area of ΔABC= 21

×AC×BC (by i)

= 21

×6×8cm 2

=24cm 2

.

Now, Area of shaded region = Area of circle − area of ΔABC

=(78.5−24)cm 2

=54.5cm2

.

@Marzi......