CBSE Class 10-Mathematics: Chapter –12 Areas Related to Circles Part 24
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Question 23:
A chord of a circle of radius subtends an angle of at the center. Find the area of the corresponding segment of the circle.

A Chord of a Circle of Radius
Answer:
Here,
Area of corresponding sector
For, Area of ,
Draw
In right triangles OMA and OMB,
[Radii of same circle]
[Common]
In right angled triangle OMA,
Also,
Area of corresponding segment Area of corresponding sector – Area of
Unless stated otherwise, take
Question 24:
Find the area of the shaded region in figure, if , and is the centre of the circle.

Find the Area of the Shaded Region
Answer:
[Angle in semicircle is ]
Radius of the circle
Area of the semicircle
Area of right triangle
Area of shaded region Area of semicircle Area of right triangle RPQ