M l aggarwal understanding icse mathematics class 9 Solutions for Chapter 15 circle

Calculate the length of a chord which is at a distance of 12 cm from the centre of a

circle of radius 13 cm.

A chord of length 8 cm is at a distance of 3 cm from the centre of the circle.

Calculate the radius of the circle.

Calculate the length of the chord which is at a distance of 6 cm from the centre of a

circle of diameter 20 cm.

A chord of length 16 cm is at a distance of 6 cm from the centre of the circle. Find

the length of the chord of the same circle which is at a distance of 8 cm from the

centre.

In a circle of radius 5 cm, AB and CD are two parallel chords of length 8 cm and 6 cm

respectively. Calculate the distance between the chords if they are on :

(i) the same side of the center.

(ii) the opposite sides of the centre

(a) In the figure given below, O is the center of the circle. AB and CD are two chords of the circle, OM is perpendicular to AB and ON is

perpendicular to CD. AB = 24 cm,

OM = 5 cm, ON = 12 cm. Find the:

(i) the radius of the circle.

(ii) length of chord CD.

(b) In the figure (ii) given below, the CD is the diameter which meets the chord AB in E

such that AE = BE = 4 cm. If CE = 3 cm, find the radius of the circle.

that

ABC is an isosceles triangle inscribed in a circle. If AB = AC = 12√5 cm and BC = 24

cm, find the radius of the circle.

An equilateral triangle of side 6 cm is inscribed in a circle. Find the radius of the

circle.

If arcs APB and CQD of a circle are congruent, then find the ratio of AB: CD.

A and B are points on a circle with center O. C is a point on the circle such that OC

bisects ∠AOB, prove that OC bisects the arc AB.