Selina solutions for Concise Mathematics [English] Class 9 ICSE chapter 16 - Circle [Latest edition]

A chord of length 6 cm is drawn in a circle of diameter 10 cm, its distance from the centre of the circle is ______.

The given figure shows two concentric circles and AD is a chord. The relation between AB and CD is:

In the given figure, chord AB is larger than chord CD. The relation between OM and ON is:

The line joining the mid-points of two chords of a circle passes through its centre, then the chords are ______.

In the given figure, O and O' are centres of two circles, AB//CD//OO′, then which of the following is not true:

A chord of length 8 cm is drawn at a distance of 3 cm from the center of the circle.
Calculate the radius of the circle.

The radius of a circle is 17.0 cm and the length of the perpendicular drawn from its center to a chord is 8.0 cm.
Calculate the length of the chord.

A chord of length 24 cm is at a distance of 5 cm from the center of the circle. Find the length of the chord of the same circle which is at a distance of 12 cm from the center.

In the following figure, AD is a straight line, OP ⊥ AD and O is the centre of both circles. If OA = 34cm, OB = 20 cm and OP = 16 cm;
find the length of AB.

In a circle of radius 17 cm, two parallel chords of lengths 30 cm and 16 cm are drawn. Find the distance between the chords, if both the chords are:

1. on the opposite sides of the centre;
2. on the same side of the centre.

Two parallel chords are drawn in a circle of diameter 30.0 cm. The length of one chord is 24.0 cm and the distance between the two chords is 21.0 cm;

find the length of another chord.

A chord CD of a circle whose center is O is bisected at P by a diameter AB. Given OA = OB = 15 cm and OP = 9 cm.
Calculate the lengths of: (i) CD ; (ii) AD ; (iii) CB.

A straight line is drawn cutting two equal circles and passing through the mid-point M of the line joining their centers O and O'. Prove that the chords AB and CD, which are intercepted by the two circles, are equal.

M and N are the mid-points of two equal chords AB and CD respectively of a circle with center O.
Prove that: (i) ∠BMN = ∠DNM
                  (ii) ∠AMN = ∠CNM

Two equal chords AB and CD of a circle with center O, intersect each other at point P inside the circle.
Prove that: (i) AP = CP ; (ii) BP = DP

In the following figure, OABC is a square. A circle is drawn with O as centre which meets OC at P and OA at Q.
Prove that:
( i ) ΔOPA ≅ ΔOQC 
( ii ) ΔBPC ≅ ΔBQA

The length of the common chord of two intersecting circles is 30 cm. If the diameters of these two circles are 50 cm and 34 cm, calculate the distance between their centers.

The line joining the midpoints of two chords of a circle passes through its center.

Prove that the chords are parallel.

In the following figure, the line ABCD is perpendicular to PQ; where P and Q are the centers of the circles.
Show that:
(i) AB = CD ;
(ii) AC = BD.

In the given figure, arc APB = arc CQD, then:

In the given figure, O is centre of the circle and ∠COD is greater than ∠AOB, then:

In a circle, O is its centre and AB, CD are B its two chords. If AB : CD = 3 : 2, then ratio between ∠AOB and ∠COD is ______.

In the given figure, O is centre of the circle and ABC is an equilateral triangle, then ∠AOB is equal to:

In the given figure, O is centre of the circle and chord AB : chord CD = 5 : 3. If angle DOC = 60°; then ∠AOB is:

In the given figure, a square is inscribed in a circle with center O. Find:

1. ∠BOC
2. ∠OCB
3. ∠COD
4. ∠BOD

Is BD a diameter of the circle?

In the given figure, AB is a side of regular pentagon and BC is a side of regular hexagon.
(i) ∠AOB
(ii) ∠BOC
(iii) ∠AOC
(iv) ∠OBA
(v) ∠OBC
(vi) ∠ABC

In the given figure, arc AB and arc BC are equal in length. If ∠AOB = 48°, find:
(i) ∠BOC
(ii) ∠OBC
(iii) ∠AOC
(iv) ∠OAC

In the given figure, the lengths of arcs AB and BC are in the ratio 3:2. If ∠AOB = 96°, find: 

1. ∠BOC
2. ∠ABC

In the given figure, AB = BC = DC and ∠AOB = 50°.
(i) ∠AOC
(ii) ∠AOD
(iii) ∠BOD
(iv) ∠OAC
(v) ∠ODA

In the given figure, AB is a side of a regular hexagon and AC is a side of a regular eight-sided polygon.
Find:
(i) ∠AOB
(ii) ∠AOC
(iii) ∠BOC 
(iv) ∠OBC

In the given figure, O is the center of the circle and the length of arc AB is twice the length of arc BC. If ∠AOB = 100°,
find: (i) ∠BOC (ii) ∠OAC

In a circle with centre at point O, chord AB is a side of a square and chord BC is a side of regular hexagon. Then angle AOC is equal to ______.

AB (= 20 cm) is diameter of the given circle and AP (= 16 cm). The distance of chord AP from centre O is ______.

Given O is centre of the circle with chord AB = 8 cm. OA = 5 cm and OD ⊥ AB. The length of CD is ______.

AB and CD are chords of a circle with centre O, ∠AOB = 60° and angle ∠COD = 45°: the ratio between the lengths of chords AB and CD is ______.

Statement (1): O and O' are centres of two equal circles and ABCD is a straight line.

Statement (2): If OР ⊥ АВ, O'Q ⊥ CD and O'Q is greater than OP, then CD > AB.

Statement (1): In a circle with centre O, chord AB: chord BC = 1 : 3. If angle AOC is 160° ⇒ angle BOC = 120°.

Statement (2): AB : BC = 1 : 3 ⇒ ∠AOC = 3 × ∠AOB

Assertion (A): In the given figure, chord AB = 8 cm, diameter CD = 20 cm, then length of OP = 10 cm.

Reason (R): OP = `sqrt(OA^2 - AP^2)` and CP = OC + OP.

The figure given below, shows a circle with centre O in which diameter AB bisects the chord CD at point E. If CE = ED = 8 cm and EB = 4 cm, find the radius of the circle.

In the given figure, O is the centre 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:

1. radius of the circle.
2. length of chord CD.

AB and CD are two equal chords of a circle with center O which intersect each other at a right angle at point P.
If OM ⊥ AB and ON ⊥ CD;
show that OMPN is a square.

The radius of a circle is 13 cm and the length of one of its chords is 24 cm.
Find the distance of the chord from the center.

Prove that equal chords of congruent circles subtend equal angles at their center.

Draw two circles of different radii. How many points these circles can have in common? What is the maximum number of common points?

Suppose you are given a circle. Describe a method by which you can find the center of this circle.

Given two equal chords AB and CD of a circle with center O, intersecting each other at point P.
Prove that:
(i) AP = CP
(ii) BP = DP 

In a circle of radius 10 cm, AB and CD are two parallel chords of lengths 16 cm and 12 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 center.

In the given figure, O is the center of the circle with radius 20 cm and OD is perpendicular to AB. If AB = 32 cm,
find the length of CD.

In the given figure, AB and CD are two equal chords of a circle, with centre O. If P is the mid-point of chord AB, Q is the mid-point of chord CD and ∠POQ = 150°, find ∠APQ.

In the given figure, AOC is the diameter of the circle, with centre O. If arc AXB is half of arc BYC, find ∠BOC.

The circumference of a circle, with center O, is divided into three arcs APB, BQC, and CRA such that:
`"arc APB"/2 = "arc BQC"/3 = "arc CRA"/4`

Find ∠BOC.