ICSE Guess > ICSE/ISC eBooks > Class X > Maths by Mr. M. P. Keshari

ICSE / ISC eBooks

Exercise – 18

Q.1. Calculate the length of a chord which is at a distance of 12cm from the centre of a circle of radius 13cm.

Q.2. The chord of a circle of radius 17cm is 30cm. Find the distance of the chord from the centre of the circle.

Q.3. Two equal chords AB and CD of a circle intersect at P, show that AP = PD and BP = PC.

Q.4. AB and CD are two parallel chords of a circle on the same side of the centre. If AB = 6cm, CD = 12cm and distance between then is 3cm. Find the radius of the circle.

Q.5. Two chords of length 10cm and 24cm of a circle are parallel. If the distance between them is 7cm, find the diameter of the circle.

Q.6. In a circle of radius 13cm, AB and CD are two parallel chords of length 24cm and 10cm respectively. Calculate the distance between the chords, if they are on

1. The same side of the centre
2. Opposite side of the centre.

Q.7. A chord 4x long is (x - 1) away from the centre of the circle whose radius is (2x + 1) long. Find the radius and length of the chords.

Q.8. AB and CD are two equal chords of a circle with centre O, intersecting at a point x within the circle. Prove that OX bisects

Q.9. In a circle of radius 5cm, AB and AC are two chords equal in length of 6cm. Find the length of the chord BC.

Q.10. Find the length of a chord which is at a distance of 4cm from the centre of a circle of radius 5cm.

Q.11. Find the locus of the middle points of equal chords of a circle

Q.12. In the adjoining fig; CD is a diameter which meets chord AB at E such that AE = BE = 4cm.If CE = 3cm, find the radius of the circle.

Q.13. If a line l intersects two concentric circles at the points A, B, C and D as shown in the figure. Prove that AB = CD.

Q.14. In the given figure, L and M are mid-points of two equal chords AB and CD of a circle with centre O. Prove that.

Q.15. In an equilateral triangle, prove that the centroid and the circumference of the triangle coincide.

Answers

1. 10cm	2. 8cm
5. 26cm	6. (i) 7cm (ii) 17cm
7. 13 units, 24 units	9. 9.6cm
10. 6cm	11. The locus is a circle concentric with original circle with original circle with radius equal to the distance of chord from the centre.
12.