CBSE Class 10-Mathematics: Chapter – 12 Areas Related to Circles Part 24 (For CBSE, ICSE, IAS, NET, NRA 2023)

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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