M l aggarwal understanding icse mathematics class 10 Solutions for Chapter 14 circles

Exercises in Chapter 14 circles Grade 10

Circles Exercise 15.1

Circles Exercise 15.2

Circles Exercise 15.3

Questions in Circles Exercise 15.1

Using the given information, find the value of x in each of the following figures:

If O is the center of the circle, find the value of x in each of the following figures (using the given information):

Using the given information, find the value of x in each of the following figures:

If O is the center of the circle, find the value of x in each of the following figures (using the given information):

In the figure (ii) given below, O is the centre of the circle. If ∠AOB = 140° and ∠OAC = 50°, find ∠ACB

In the figure (ii) given below, O is the centre of the circle. If ∠AOB = 140° and ∠OAC = 50°, find ∠OBC

In the figure (i) given below, calculate the values of x and y.

In the figure (ii) given below, O is the centre of the circle. Calculate the values of x and y.

In the figure (i) given below, M, A, B, N are points on a circle having centre O. AN and MB cut at Y. If ∠NYB = 50° and ∠YNB = 20°, find ∠MAN and the reflex angle MON.

In the figure (ii) given below, it is given that O is the centre of the circle and ∠AOC = 130°. Find ∠ ABC

In the figure (ii) given below, O is the centre of the circle. If ∠AOB = 140° and ∠OAC = 50°, find ∠OAB

In the figure (ii) given below, O is the centre of the circle. If ∠AOB = 140° and ∠OAC = 50°, find ∠CBA

In the figure (i) given below, AD || BC. If ∠ACB = 35°. Find the measurement of ∠DBC.

In the figure (i) given below, O is the centre of the circle and ∠PBA = 42°. Calculate the value of ∠PQB

In the figure (ii) given below, AB is a diameter of the circle whose centre is O. Given that ∠ECD = ∠EDC = 32°, calculate ∠CEF

In the figure (ii) given below, AB is a diameter of the circle whose centre is O. Given that ∠ECD = ∠EDC = 32°, calculate ∠COF.

In the figure (i) given below, AB is a diameter of the circle APBR. APQ and RBQ are straight lines, ∠A = 35°, ∠Q = 25°. Find (i) ∠PRB (ii) ∠PBR (iii) ∠BPR.

In the figure (ii) given below, it is given that ∠ABC = 40° and AD is a diameter of the circle. Calculate ∠DAC.

In the figure given below, O is the circumcenter of triangle ABC in which AC = BC. Given that ∠ACB = 56°, calculate ∠CAB

In the figure given below, O is the circumcenter of triangle ABC in which AC = BC. Given that ∠ACB = 56°, calculate ∠OAC.

In the figure given below, P and Q are centers of two circles intersecting at B and C. ACD is a straight line. Calculate the numerical value of x.

Questions in Circles Exercise 15.2

In the figure (ii) given below, ABCD is a cyclic trapezium in which AD is parallel to BC and ∠B = 70°, find: ∠BAD

If O is the center of the circle, find the value of x in each of the following figures (using the given information)

In the figure (if) given below, AB is parallel to DC, ∠BCE = 80° and ∠BAC = 25°. Find: ∠CAD

In the figure (i) given below, AC is a diameter of the given circle and ∠BCD = 75°. Calculate the size of ∠ABC

In the figure, (i) given below, if ∠DBC = 58° and BD is a diameter of the circle, calculate: ∠BDC

In the figure, (i) given below, if ∠DBC = 58° and BD is a diameter of the circle, calculate: ∠BEC

In the figure, (i) given below, if ∠DBC = 58° and BD is a diameter of the circle, calculate: ∠BAC

In the figure (if) given below, AB is parallel to DC, ∠BCE = 80° and ∠BAC = 25°. Find: ∠CBD

In the figure (if) given below, AB is parallel to DC, ∠BCE = 80° and ∠BAC = 25°. Find: ∠ADC (2008)

In the figure (ii) given below, ABCD is a cyclic trapezium in which AD is parallel to BC and ∠B = 70°, find:∠BCD.

In the figure given below, O is the center of the circle. If ∠BAD = 30°, find the values of p, q and r.

In the figure given below, PQ is a diameter. Chord SR is parallel to PQ.Given ∠PQR = 58°, calculate ∠RPQ

(T is a point on the minor arc SP)

In the figure given below, PQ is a diameter. Chord SR is parallel to PQ.Given ∠PQR = 58°, calculate ∠STP

(T is a point on the minor arc SP)

In the figure (i) given below, AB is a diameter of the circle. If ∠ADC = 120°, find ∠CAB.

In the figure (ii) given below, sides AB and DC of a cyclic quadrilateral ABCD are produced to meet at E, the sides AD and BC are produced to meet at F. If x : y : z = 3 : 4 : 5, find the values of x, y and z.

In the figure given below, two circles intersect at points P and Q. If ∠A = 80° and ∠D = 84°, calculate ∠QBC and ∠BCP

In the figure (i) given below, AC is a diameter of the given circle and ∠BCD = 75°. Calculate the size of ∠EAF.

Questions in Circles Exercise 15.3

In figure (i) given below, quadrilateral ABCD is circumscribed; find the perimeter of quadrilateral ABCD.

The tangent to a circle of radius 6 cm from an external point P, is of length 8 cm. Calculate the distance of P from the nearest point of the circle.

Find the length of the tangent drawn to a circle of radius 3cm, from a point distnt 5cm from the center.

A point P is at a distance 13 cm from the center C of a circle and PT is a tangent to the given circle. If PT = 12 cm, find the radius of the circle.

Two concentric circles are of the radii 13 cm and 5 cm. Find the length of the chord of the outer circle which touches the inner circle.

Two circles of radii 5 cm and 2.8 cm touch each other. Find the distance between their centers if they touch :

externally

Two circles of radii 5 cm and 2-8 cm touch each other. Find the distance between their centers if they touch : internally.

In figure (i) given below, triangle ABC is circumscribed, find x.

In figure (ii) given below, quadrilateral ABCD is circumscribed, find x.

In figure (ii) given below, quadrilateral ABCD is circumscribed and AD ⊥ DC ; find x if radius of incircle is 10 cm.

In the figure (ii) given below, from an external point P, tangents PA and PB are drawn to a circle. CE is a tangent to the circle at D. If AP = 15 cm, find the perimeter of the triangle PEC.

If a, b, c are the sides of a right triangle where c is the hypotenuse, prove that the radius r of the circle which touches the sides of the triangle is given by r = /frac (a + b – c) – (2)

Three circles of radii 2 cm, 3 cm and 4 cm touch each other externally. Find the perimeter of the triangle obtained on joining the centers of these circles.