Question

The diagram given shows triangle ABC inscribed in a circle
. AB is the diametre of the circle, AC - 16 cm and BC = 12 cm.
ZC = 90°
(1) Find the diametre of the circle AB
(11) Find the area of 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 =

2

d

=

2

10

cm=5 cm.

i.e The Area of circle =πr

2

=3.14×5

2

cm

2

=78.5cm

2

.

Again, Area of ΔABC=

2

1

×AC×BC (by i)

=

2

1

×6×8cm

2

=24cm

2

.

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

=(78.5−24)cm

2

=54.5cm

2

.