NCERT Class 10 Chapter 12 Areas Related to Circles CBSE Board Sample Problems Long Answer
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Question
All the vertices of a rhombus lie on a circle. Find the area of rhombus, if the area of circle is
Solution

Rhombus Lie on a Circle
Diagonal of a rhombus are perpendicular bisector of each other. D
Each diagonal is diameter of the circle.
Now. Area of circle
:. Diameter of the circle = 40 cm = each diagonal of the rhombus
Area of the circle
Question
Find the area of the minor segment of a circle of radius 14 cm, when its central angle is . Also find the area of the corresponding major segment.
Solution

Circle of Radius 14 Cm
In
Also AO=BO
is an equilateral triangle.
Area of equilateral
Area of sector
Area of minor segment
Area of circle
Area of major segment
Question
In figure, APB and AQO are semicircle, and AC = OB. If the perimeter of the figure is 40 cm, find the area of the shaded region.

APB and AQO Are Semicircle
Solution
Let r be the radius of the semicircle APB, i.e. OB = OA = r, then is the radius of the semicircle AQO.
Given Penmeter of the figure is 40cm.
... Length of are APB + length of are
Now, area of shaded portion - area of semicircle APLI + area of semicircle AQO
By putting r=7cm
Required area of shaded
Portion is
Question
Solution
In Figure, is Shown a Sector OAP of a Circle with Centre O, Containing is Perpendicular to the Radius OA and Meets OP Produced at B. Prove That the Perimeter of Shaded Region is Ution
Length are
Perimeter of shaded region
Question
An elastic belt is placed around the rim of a pulley of radius 5 cm. From one point C on the belt, the elastic belt is pulled directly away from the centre O of the pulley until it is at P, 10 cm from the point O. Find the length of the belt that is still in contact with the pulley. Also find the shaded area, (use and )

An Elastic Belt
Solution

An Elastic Belt
Given: AO = 5 cm and OP = 10 cm
In right,
Length 0f
Hence, length of belt in contact
Now, in right OAT we have
Area of sector OACB
Shaded Area = Area of — Area of OACB
Question
A wire is in the form of a circle of radius 28cm. It is rebent into a square form. Find the length of the side of the square
Solution
Length of the wire= circumference of the circle
Let each side of the square be x cm
Perimeter = length of the wire
Question
The sum of radii of two circles is 140cm and the difference of their circumference is 88cm. Find the diameters of the circles.
Solution
Let radius of first circle be r cm.
Radius of second circle
Circumference of first circle
Circumference of second circle
Difference of two circumference
Radius of second circle
Diameter of first circle
Diameter of second circle
Question
PQRS is a diameter of a circle of radius 6 cm. The length PQ, QR and RS are equal. Semi-circles are drawn on PQ and QS as diameters as shown in the figure. Find the area and perimeter of the shaded region.

Diameter of a Circle of Radius 6 Cm
Solution
Perimeter=ir6 + ir4 + ir2 = l2ir
= 37.68 cm
Area of the shaded region