Areas related to Circles ncert solutions Chapter 12 Exercise 12.2 Question 5
5. In a circle of radius 21 cm, an arc subtends an angle of
at the center. Find:
(i) the length of the arc (ii) area of the sector formed by the arc
(iii) area of the segment formed by the corresponding chord
Solution:
is the angle subtended by arc at the center of circle and r is the radius of circle.
Length of arc
cm
Area of sector formed by arc AB=
Area of segment formed by arc AB= Area shaded in light blue
= Area of minor sector – area of triangle AOB (1)
In
,
AO=OB {radii of circle}
{Angles opposite to equal sides are equal}
Also, we have
{Angle sum property of triangle}
Therefore,
which means that
is an equilateral triangle.
Area of Equilateral Triangle =
(2)
Putting equation (2) in (1), we get
Area of segment formed by arc AB= Area of minor sector – area of
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