Exams › SSC CGL (Prelims) › General

A chord of a circle has length 16 cm. The angle subtended by the chord at a point on the circumference is \(45^\circ\). What is the distance from the center of the circle to the chord?

1. 8\sqrt{2} cm
2. 4\sqrt{2} cm
3. 8 cm
4. 4 cm

Correct answer: 8 cm

Solution

The angle subtended by the chord at the center is twice the angle at the circumference, so it is \(90^\circ\). The perpendicular from the center to the chord bisects it, giving a right triangle with hypotenuse equal to the radius and one leg 8 cm. The distance from the center to the chord comes out to 8 cm.

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?
• 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 $120^\circ$?
• 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?

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