Exams › SSC CGL (Prelims) › General

What is the area of the segment formed by a chord in a circle of radius 10 cm when the angle subtended at the centre is $120^\circ$?

1. $\frac{100\pi}{3}-25\sqrt{3}$
2. $\frac{100\pi}{3}-50\sqrt{3}$
3. $50\pi-25\sqrt{3}$
4. $50\pi-50\sqrt{3}$

Correct answer: $\frac{100\pi}{3}-25\sqrt{3}$

Solution

The area of the sector is $\frac{120}{360}\pi(10)^2=\frac{100\pi}{3}$. The area of the triangle formed by the two radii is $\frac12\cdot 10\cdot 10\cdot \sin 120^\circ=25\sqrt{3}$. Subtracting gives the segment area $\frac{100\pi}{3}-25\sqrt{3}$.

Related SSC CGL (Prelims) General questions

• Two circles have radii 14 cm and 6 cm. If the length of a direct common tangent is 24 cm, what is the distance between their centers?
• The distance between the centres of two circles is $d$. The lengths of the direct and transverse common tangents are $L$ and $M$ respectively. If $L^2 + M^2 = 320$ and the sum of the squares of the radii is 160, what is $d$?
• Two parallel chords of lengths 20 cm and 14 cm lie on the same side of the centre of a circle. The distance between them is 3 cm. What is the radius of the circle?
• Two equal chords, PQ and RS, are at a distance of 12 cm from the center of a circle. If the radius is 20 cm, what is the length of PQ?
• A circular disc is divided into 6 equal sectors. If the area of one sector is 66 cm², what is the radius of the disc?
• If two circles touch externally, how many common tangents do they have?

⚔️ Practice SSC CGL (Prelims) General free + battle 1v1 →