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Mathematics

Area of a Segment of a Circle

A chord of a ...

Question

A chord of a circle of radius 12 cm subtends an angle of 120° at the centre. Find the area of the corresponding segment of the circle.

[Use π = 3.14 and]

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Solution

Let us draw a perpendicular OV on chord ST. It will bisect the chord ST.

SV = VT

In ΔOVS,

Area of ΔOST =

Area of sector OSUT =

Area of segment SUT = Area of sector OSUT − Area of ΔOST

= 150.72 − 62.28

= 88.44 cm²

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A chord of a circle of radius 12 cm subtends an angle of 120° at the centre. Find the area of the corresponding segment of the circle. [Use π = 3.14 and]

Let us draw a perpendicular OV on chord ST. It will bisect the chord ST. SV = VT In ΔOVS, Area of ΔOST = Area of sector OSUT = Area of segment SUT = Area of sector OSUT − Area of ΔOST = 150.72 − 62.28 = 88.44 cm2

A chord of a circle of radius 12 cm subtends an angle of 120° at the centre. Find the area of the corresponding segment of the circle.

[Use π = 3.14 and]

Let us draw a perpendicular OV on chord ST. It will bisect the chord ST.

SV = VT

In ΔOVS,

Area of ΔOST =

Area of sector OSUT =

Area of segment SUT = Area of sector OSUT − Area of ΔOST

= 150.72 − 62.28

= 88.44 cm²