# MCQs for Mathematics Class 10 with Answers Chapter 10 Circles

Students of class 10 Mathematics should refer to MCQ Questions Class 10 Mathematics Circles with answers provided here which is an important chapter in Class 10 Mathematics NCERT textbook. These MCQ for Class 10 Mathematics with Answers have been prepared based on the latest CBSE and NCERT syllabus and examination guidelines for Class 10 Mathematics. The following MCQs can help you to practice and get better marks in the upcoming class 10 Mathematics examination

**Chapter 9 Circles MCQ with Answers Class 10 Mathematics**

MCQ Questions Class 10 Mathematics Circles provided below have been prepared by expert teachers of grade 10. These objective questions with solutions are expected to come in the upcoming Standard 10 examinations. Learn the below provided MCQ questions to get better marks in examinations.

**Question. Two circle touch each other externally at C and AB is a common tangent to the circles. Then,∠ACB = **

(a) 60°

(b) 45°

(c) 30°

(d) 90°

**Answer**

D

**Question. If tangents PA and PB from a point P to a circle with centre O are inclined to each other at anangle of 80° then ∠POA is equal to **

(a) 50°

(b) 60°

(c) 70°

(d) 80°

**Answer**

A

**Question. A circle with centre O is inscribed in a right angle triangle ABC, right angled at B. If BC = 15 cm, AC = 17 cm, the radius ‘r’ of the circle is : **

(a) 2 cm

(b) 2.5 cm

(c) 3 cm

(d) 5 cm

**Answer**

C

**Question. If TP and TQ are two tangents to a circle with centre O so that ∠POQ = 110°, then, ∠PTQ is equalto **

(a) 60°

(b) 70°

(c) 80°

(d) 90°

**Answer**

B

**Question. The length of a tangent drawn from a point at a distance of 10 cm of circle is 8 cm. The radius ofthe circle is **

(a) 4 cm

(b) 5 cm

(c) 6 cm

(d) 7 cm

**Answer**

C

**Question. Tangents from an external point to a circle are **

(a) equal

(b) not equal

(c) parallel

(d) perpendicular

**Answer**

A

**Question. PQ is a tangent drawn from a point P to a circle with centre O and QOR is a diameter of the circle such that <POR = 120°, then <OPQ is : **

(a) 45°

(b) 60°

(c) 90°

(d) 30°

**Answer**

D

**Question. Two parallel lines touch the circle at points A and B respectively. If area of the circle is 25 n cm 2 ,then AB is equal to **

(a) 5 cm

(b) 8 cm

(c) 10 cm

(d) 25 cm

**Answer**

C

**Question. A line through point of contact and passing through centre of circle is known as **

(a) tangent

(b) chord

(c) normal

(d) segment

**Answer**

C

**Question. Segment joining the points of contact of two parallel tangents **

(a) may or may not pass through the centre.

(b) will pass through the centre.

(c) will not pass through the centre.

(d) none of these

**Answer**

B

**Question. At point A on a diameter AB of a circle of radius 10 cm, tangent XAY is drawn to the circle. Thelength of the chord CD parallel to XY at a distance 16 cm from A is **

(a) 8 cm

(b) 10 cm

(c) 16 cm

(d) 18 cm

**Answer**

C

**Question. Number of tangents drawn at a point of the , circle is/are **

(a) one

(b) two

(c) none

(d) infinite

**Answer**

A

**Question. PQ is a chord of length 8 cm of a circle of radius 5 cm. The tangents at P and Q intersect at a point P. The length of TP is : **

(a) 5 cm

(b) 5 2/ 3 cm

(c) 6 cm

(d) 6 2/3 cm

**Answer**

D

**Question. A circle touches all the four sides of a quadrilateral ABCD, with AB = 7 cm, BC = 8 cm and CD = 5 cm. The length of AD is : **

(a) 3 cm

(b) 4 cm

(c) 5 cm

(d) 6 cm

**Answer**

B

**Question. A tangent is drawn from a point at a distance of 17 cm of circle C(0, r) of radius 8 cm. The lengthof its tangent is **

(a) 5 cm

(b) 9 cm

(c) 15 cm

(d) 23 cm

**Answer**

C

**Question. The maximum number of common tangents that can be drawn to two circles intersecting at twodistinct point is **

(a) 2

(b) 4

(c) 1

(d) 3

**Answer**

A

**Question. A tangent PQ at a point P of a circle of radius 5 cm meets a line through the centre O at a point Q **

(a) √119 cm

(b) 13 cm

(c) 12 cm

(d) 8.5 cm

**Answer**

A

**Question. In a circle of radius 7cm, tangent PT is drawn from point P such that PT = 24cm. If O is the centreof the circle, then the length of OP is: **

(a) 30cm

(b) 31cm

(c) 28cm

(d) 25cm

**Answer**

D

**Question. The length of a tangent from a point 25 cm from the centre of a circle is 24 cm. The radius of the circle is: **

(a) 5 cm

(b) 7 cm

(c) 10 cm

(d) 12 cm

**Answer**

B

**Question. If four sides of a quadrilateral ABCD are tangential to a circle, then **

(a) AC + AD = BD + CD

(b) AB + CD = BC + AD

(c) AB + CD = AC + BC

(d) AC + AD = BC + DB

**Answer**

B

**Question. A tangent PQ at a point P of a circle of radius 8 cm meets a line through the centre O at a point Q such that OQ = 15 cm. Length PQ is : **

(a) 17 cm

(b) 10 cm

(c) 125 cm

(d) none of these

**Answer**

A

**Question. The tangents drawn at the extremities of the diameter of a circle are **

(a) perpendicular

(b) parallel

(c) equal

(d) none of these

**Answer**

B

**Question. From a point P which is at a distance of 13 cm from the centre O of a circle of radius 5 cm, thepair of tangents PQ and PR to the circle are drawn. Then the area of the quadrilateral PQOR is **

(a) 60 cm^{ 2}

(b) 65 cm^{ 2}

(c) 30 cm^{2 }

(d) 32.5 cm^{ 2}

**Answer**

A

**Question. A circle touches all the four sides of a quadrilateral ABCD. Then, **

(a) AB + CD = AC + BC

(b) AB + CD = BC + AD

(c) AC + AD = BD + CD

(d) AC + BD = BC + DB

**Answer**

B

**Question. Two circle touch each other externally at C and AB is a common tangent to the circles. Then,∠ACB = **

(a) 60°

(b) 45°

(c) 30°

(d) 90°

**Answer**

D

**Question. PQ is a tangent drawn from a point P to a circle with centre O and QOR is a diameter of the circlesuch that ∠POR = 120°, then ∠OPQ is **

(a) 60°

(b) 45°

(c) 30°

(d) 90°

**Answer**

C

**Question. Two circles touch each other externally at C and AB is a common tangent to the circles. Then, <ACB is: **

(a) 60°

(b) 45°

(c) 30°

(d) 90°

**Answer**

D

**Question. Two circles of radii 10 cm and 8 cm are concentric. The length of a chord of the larger circle which touches the smaller is : **

(a) 6 cm

(b) 11 cm

(c) 12 cm

(d) 13 cm

**Answer**

C

**Question. The length of tangents drawn from an external point to the circle **

(a) are equal

(b) are not equal

(c) sometimes are equal

(d) are not defined

**Answer**

A

**Question. If TP and TQ are tangents to a circle with centre O such that <POQ = 110°, then <PTQ is equal to : **

(a) 60°

(b) 70°

(c) 80°

(d) 90°

**Answer**

B

We hope the above multiple choice questions for Class 10 Mathematics for Chapter 9 Circles provided above with answers based on the latest syllabus and examination guidelines issued by CBSE, NCERT and KVS are really useful for you. Circles is an important chapter in Class 10 as it provides very strong understanding about this topic. Students should go through the answers provided for the MCQs after they have themselves solved the questions. All MCQs have been provided with four options for the students to solve. These questions are really useful for benefit of class 10 students. Please go through these and let us know if you have any feedback in the comments section.