CBSE Class 10-Mathematics: Chapter – 12 Areas Related to Circles Part 18 (For CBSE, ICSE, IAS, NET, NRA 2023)

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Question 8:

In the given figure is an equilateral triangle inscribed in a circle of radius 4 cm and center O. Show that the area of the shaded region is .

Answer:

In , Let ,

Area of shaded region Area of sector Area of

Question 9:

The radii of two circles are and respectively. Find the radius of the circle having its area equal to the sum of the areas of the two circles.

Answer:

Area of the first circle

Total area

Let R be the radius of the circle with area

Hence, required radius

Question 10:

A chord of a circle of radius subtends a right angle at the centre. Find the area of the corresponding: (Use

(i) Minor sector

(ii) Major sector

(iii) Minor segment

(iv) Major segment

Answer:

(i) Minor sector

Area of minor sector

(ii) Major sector

Area of major sector Area of circle – Area of minor sector

(iii) Minor segment

We know that area of minor segment

Area of minor sector Area of

(iv) Area of major segment = Area of the circle – Area of minor segment