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Question

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

A
yes, it is true for minor segment since ar.minor segment = ar.sector-triangle made by the radii and the chord of the segment.
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B
Yes, it is only true for major segment since ar.minor segment = ar.sector-triangle made by the radii and the chord of the segment
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C
No, it is only true for major segment since ar.minor segment
=ar.sector-triangle made by the radii and the chord of the segment.
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D
No, it is only true for minor segment since ar.minor segment
=ar.sector-triangle made by the radii and the chord of the segment.
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Solution

The correct option is D No, it is only true for minor segment since ar.minor segment
=ar.sector-triangle made by the radii and the chord of the segment.
GivenABisthechordofthecirclewithcentreO.TheminorsegmentisABP&theminorsectorisAOBP.AlsothemajorsegmentisABQ&themajorsectorisABQ.Tofindoutthevalidityofthestatementthatar.segment<ar.sector.SolutionInthefigurear.minorsegmentABP=ar.minorsectorAOBPar.ΔOABar.minorsegmentABP<ar.minorsectorAOBP.Again,inthefigure,ar.majorsegmentABQ=ar.majorsectorABQ+ar.ΔOAB.ar.majorsegment>ar.majorsector.Thestatemenisvalidonlyforminorsegment.AnsOptionD.
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