Is it true to say that area of a segment of a circle is less than the area of its corresponding sector? Why

Solution:

We know that

AB is the chord of circle with O as the centre

The minor sector is AOBP and the minor segment is ABP

The major sector is AOBQ and the major segment is ABQ

We have to find if area of segment is less than the area of its corresponding sector

From the figure

Area of minor segment ABP = Area of minor sector AOBP - area of triangle OAB

Area of minor segment ABP < Area of minor sector AOBP

From the figure

Area of major segment ABQ = Area of major sector AOBQ + Area of triangle OAB

Area of segment > Area of major sector

The statement is true only for minor segment

Therefore, the statement is false.

✦ Try This: Say true or false. The length of a rope by which a cow must be tethered in order that it may be able to graze an area of 616 cm² is 18 cm.

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

NCERT Exemplar Class 10 Maths Exercise 11.2 Problem 4

Is it true to say that area of a segment of a circle is less than the area of its corresponding sector? Why

Summary:

The statement “area of a segment of a circle is less than the area of its corresponding sector” is true in case of minor segment. For major segment, the area is greater than the area of the sector.

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