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Home » AB is a chord of a circle with center O and radius . AB is of length and divides the circle into two segments. Find the area of the minor segment.
AB is a chord of a circle with center O and radius 4cm. AB is of length 4cm and divides the circle into two segments. Find the area of the minor segment.
Areas Related To Circles | CBSE | Class 10 | Exercise 15.3 | Maths | RD Sharma
AB is a chord of a circle with center O and radius 4cm. AB is of length 4cm and divides the circle into two segments. Find the area of the minor segment.

As per the given data in the question,

Radius of the circle with center ‘O’, r=4cm=OA=OB

Length of the chord AB=4cm

Thus, OAB is an equilateral triangle and angle AOB={{60}^{\circ }}

So, the angle subtended at center \theta ={{60}^{\circ }}

Area of the minor segment = (Area of sector) - (Area of triangle AOB)

=\frac{\theta }{360}\times \pi {{r}^{2}}-\frac{\sqrt{3}}{4}{{\left( side \right)}^{2}}

=\frac{60}{360}\times \pi {{4}^{2}}-\frac{\sqrt{3}}{4}{{\left( 4 \right)}^{2}}

=\left( 8\pi /3-4\sqrt{3} \right)=8.37-6.92=1.45c{{m}^{2}}

Hence, the required area of the segment is \left( 8\pi /3-4\sqrt{3} \right)c{{m}^{2}}

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