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Area of a segment of a circle = area of the corresponding sector - area of the corresponding triangle. Is the following statement true? Give reasons for your answer

Solution:

We have to determine if the area of a segment of a circle = area of the corresponding sector - area of the corresponding triangle.

We know that the area of a segment of a circle is less than the area of its corresponding sector is true in case of a minor segment.

For a major segment, the area is greater than the area of its corresponding sector

Therefore, the statement is false.

✦ Try This: In a circle of radius 10.5 cm, the minor arc is one-fifth of the major arc. Find the area of the sector corresponding to the major arc.

It is given that

Radius of the circle = 10.5 cm

Consider x cm as the major arc and x/5 cm as the length of minor arc

Circumference of circle = x + x/5 = 6x/5 cm …. (1)

The formula to find the circumference of circle = 2πr

Substituting the values

= 2 × 22/7 × 10.5 …. (2)

By equating both

6x/5 = 2 × 22/7 × 10.5

x = 55 cm

So we get

Area of major sector = 1/2 × 55 × 10.5 = 288.75 cm²

Therefore, the area of the sector corresponding to the major arc is 288.75 cm².

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 12

NCERT Exemplar Class 10 Maths Exercise 11.2 Sample Problem 1

Area of a segment of a circle = area of the corresponding sector - area of the corresponding triangle. Is the following statement true? Give reasons for your answer

Summary:

The statement “Area of a segment of a circle = area of the corresponding sector - area of the corresponding triangle” is false

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