In the adjoining figure, the crescent is formed by circles which touch at the point A. O is the centre the bigger circle. If CB =9 cm and ED =5 cm. Find the area of the shaded region.

Open in App

Solution

Let O' be the centre of smaller circle
Let the diameter & Radius of bigger circle
= D & R
Let the Diameter & Radius of smaller circle
=d & r
D -d -CB =9 cm
$∴ R - r = \frac{9}{2} = 4.5$ cm =Distance between OO'.
$\Rightarrow R = r + 4.5 \Rightarrow O E = r + 4.5 = O D + 5 \Rightarrow O D = r - 0.5$

Now join O'D
O'D =r
OD =r -0.5
OO' =4.5
$\Rightarrow r^{2} = (4 - 0.5)^{2} + {4.5}^{2} r^{2} = r^{2} + \frac{1}{4} - r + {4.5}^{2}$
or $r = \frac{1}{4} + {4.5}^{2} = 20.5 c m .$
$∴ R = 20.5 + 4.5 25 c m .$
Area of shaded portha $= π (R^{2} - r^{2})$
$= π (R + r) (R - r) = π (25 + 20.5) (4.5) = 643.25 s q . c m$

Suggest Corrections

Similar questions

Q. In the figure alongside, crescent is formed by two circles which touch at the point

A

O

is the centre of the bigger circle. If radius of smaller circle is

= 5 c m

and radius of larger circle is

9 c m,

find the area of the shaded region. (Take

π = 3.14

)

In the figure, two small circles touch each other externally at the centre of a bigger circle and these small circles are touched internally by a bigger circle with radius 4 $c m$ . Find the area of the shaded region in $c m^{2}$ .

Q. In the adjoining figure, X is a point on diameter AB of the circle with centre O such that AX = 9 cm, XB = 5 cm. Find the radius of the circle (centre Y) which touches the diameter at X and touches the circle, centre O, internally at Z.

In the figure, two small circles touch each other externally at the centre of a bigger circle and these small circles are touched internally by a bigger circle with radius 4 cm. Find the area of the shaded region in cm².

Q. Find the area of the shaded region in the figure, if

A B = 5 c m, A C = 12 c m

and

O

is the centre of the circle

Join BYJU'S Learning Program