Ncert exemplar solutions mathematics class 9 Solutions for Chapter 10 circles

Exercises in Chapter 10 circles Grade 9

Circles – Exercise 10.1

Circles – Exercise 10.2

Circles – Exercise 10.3

Circles – Exercise 10.4

Questions in Circles – Exercise 10.1

In Fig. , if OA = 5 cm, AB = 8 cm and OD is perpendicular to AB, then CD is equal to:

(A) 2 cm

(B) 3 cm

(D) 5 cm

If AB = 12 cm, BC = 16 cm and AB is perpendicular to BC, then the radius of the circle passing through the points A, B and C is :

(A) 6 cm

(B) 8 cm

(D) 12 cm

In Fig., if ∠ABC = 20º, then ∠AOC is equal to:

(A) 20º

(B) 40º

(D) 10º

In Fig.10.5, if AOB is a diameter of the circle and AC = BC, then ∠CAB is equal to:

(A) 30º

(B) 60º

(D) 45º

Questions in Circles – Exercise 10.2

AD is a diameter of a circle and AB is a chord. If AD = 34 cm, AB = 30 cm, the distance of AB from the centre of the circle is :

(A) 17 cm

(B) 15 cm

(D) 8 cm

Two chords AB and CD of a circle are each at distances 4 cm from the centre. Then AB = CD

Two chords AB and AC of a circle with centre O are on the opposite sides of OA. Then ∠OAB = ∠OAC .

Two congruent circles with centres O and O’ intersect at two points A and B. Then ∠AOB = ∠AO’B.

Through three collinear points a circle can be drawn.

A circle of radius 3 cm can be drawn through two points A, B such that AB = 6 cm.

Questions in Circles – Exercise 10.3

If arcs AXB and CYD of a circle are congruent, find the ratio of AB and CD.

If the perpendicular bisector of a chord AB of a circle PXAQBY intersects the circle at P and Q, prove that arc PXA ∠ Arc PYB.

A, B and C are three points on a circle. Prove that the perpendicular bisectors of AB, BC and CA are concurrent.

AB and AC are two equal chords of a circle. Prove that the bisector of the angle BAC passes through the centre of the circle.

If a line segment joining mid-points of two chords of a circle passes through the centre of the circle, prove that the two chords are parallel.

ABCD is such a quadrilateral that A is the centre of the circle passing through B, C and D.

Prove that ∠CBD + ∠CDB = ½ ∠BAD

O is the circumcentre of the triangle ABC and D is the mid-point of the base BC. Prove that ∠BOD = ∠A.

On a common hypotenuse AB, two right triangles ACB and ADB are situated on opposite sides.

Prove that ∠BAC = ∠BDC.

Two chords AB and AC of a circle subtends angles equal to 90º and 150º, respectively at the centre. Find ∠BAC, if AB and AC lie on the opposite sides of the centre.

If BM and CN are the perpendiculars drawn on the sides AC and AB of the triangle ABC, prove that the points B, C, M and N are concyclic.

Questions in Circles – Exercise 10.4

If two equal chords of a circle intersect, prove that the parts of one chord are separately equal to the parts of the other chord.

If non-parallel sides of a trapezium are equal, prove that it is cyclic.

If P, Q and R are the mid-points of the sides BC, CA and AB of a triangle and AD is the perpendicular from A on BC, prove that P, Q, R and D are concyclic.

ABCD is a parallelogram. A circle through A, B is so drawn that it intersects AD at P and BC at Q. Prove that P, Q, C and D are concyclic.

Prove that angle bisector of any angle of a triangle and perpendicular bisector of the opposite side if intersect, they will intersect on the circumcircle of the triangle.