# Circles MCQ Class 10 Mathematics

Please refer to Chapter 9 Circles MCQ Class 10 Mathematics with answers below. These multiple-choice questions have been prepared based on the latest NCERT book for Class 10 Mathematics. Students should refer to MCQ Questions for Class 10 Mathematics with Answers to score more marks in Grade 10 Mathematics exams. Students should read the chapter Circles and then attempt the following objective questions.

**MCQ Questions Class 10 Mathematics Chapter 9 Circles**

The Circles MCQ Class 10 Mathematics provided below covers all important topics given in this chapter. These MCQs will help you to properly prepare for exams.

**Question. Two circles, both of radii a touch each other and each of them touches internally a circle of radius 2a. Then the radius of the circle which touches all the three circles is **

(a) 1/ 2 a

(b) 2/ 3 a

(c) 3/4 a

(d) a

**Answer**

B

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

(a) 50°

(b) 60°

(c) 70°

(d) 80°

**Answer**

A

**Question. In the figure, O is the centre of the circle and OA = CD, then ∠CPD is **

(a) 45°

(b) 30°

(c) 70°

(d) 60°

**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 circle such that ∠POR = 120°, then ∠OPQ is **

(a) 60°

(b) 45°

(c) 30°

(d) 90°

**Answer**

C

**Question. In figure ABCD is a cyclic quadrilateral and ∠ADC = 80°, ∠ACD = 50°, then ∠CBD is: **

(a) 60°

(b) 130°

(c) 50°

(d) 40°

**Answer**

C

**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 so that OQ = 12 cm. Length PQ is : **

(a) 12 cm

(b) 13 cm

(c) 8.5 cm

(d) √119 cm

**Answer**

D

**Question. In the given figure, AC is the diameter of the circle. ED || AC, ∠CBE = 65°, then ∠DEC is **

(a) 35°

(b) 25°

(c) 65°

(d) 30°

**Answer**

B

**Question. Three circles of radii 1, 2 and 3 units respectively touch each other externally in the plane. The circumradius of the triangle formed by joining the centers of the circles is**

(a) 1.5

(b) 2

(c) 2.5

(d) 3

**Answer**

C

**Question. Two chords AB and CD of a circle intersect each other at P outside the circle. If AB = 5 cm, BP = 3 cm and PD = 2 cm, find CD. **

(a) 4 cm

(b) 5 cm

(c) 8 cm

(d) 10 cm

**Answer**

D

**Question. Which of the following statement(s) is/are correct? **

(a) If a chord AB subtends an angle of 60° at the centre of a circle, then angle between the tangents at A and B is also 60°.

(b) The length of tangent from an external point on a circle is always greater than the radius of the circle.

(c) If a number of circle touch a given line segment PQ at a point A, then their centres lie on the perpendicular bisector of PQ.

(d) None of these

**Answer**

D

**Question. A ball is in the rest position against a step PQ. If PQ = 10 cm and QR = 15 cm, then find diameter of the ball. **

(a) 16 cm

(b) 32.5 cm

(c) 28 cm

(d) 42 cm

**Answer**

B

**Question. Circles A, B and C are externally tangent to each other and internally tangent to circle D. Circles A and B are congruent. Circle C has radius 1 unit and passes through the centre of circle D. Then are radius of circle B is ________ units. **

(a) 3/ 7

(b) 6/ 9

(c) 8 /9

(d) 9 /8

**Answer**

C

**Question. Which of the following is/are not correct? **

(a) A secant is a line that intersects a circle in two distinct points.

(b) In a circle, the perpendicular from the centre to a chord bisects the chord.

(c) The point common to a circle and its tangent is called the point of contact.

(d) Adjacent angles of a cyclic quadrilateral are supplementary.

**Answer**

D

**Question. Number of tangents to a circle which are parallel to a secant, is **

(a) 3

(b) 2

(c) 1

(d) infinite

**Answer**

B

**Question. Which of the following statement(s) is / are not correct ? **

(a) The length of tangent from an external point P on circle with centre O is always less than OP.

(b) The tangent to the circumcircle of an isosceles triangle ABC at A, in which AB = AC, is parallel to BC.

(c) If angle between two tangents drawn from a point P to a circle of radius ‘a’ and centre ‘O’is 90°, then OP = a√2.

(d) None of these

**Answer**

D

**Question. Which of the following statement(s) is/are incorrect? **

(a) Angle between the tangent line and the radius at the point of contact is 90°.

(b) A circle can have two parallel tangents atmost.

(c) The distance between two parallel tangents drawn to a circle is equal to twice of radius.

(d) A line intersecting a circle in two points is called a chord.

**Answer**

D

**Question. AB and CD are two common tangents to circles which touch each other at a point C. If D lies on AB such that CD = 4 cm, then AB is **

(a) 12 cm

(b) 8 cm

(c) 4 cm

(d) 6 cm

**Answer**

B

**Question. In fig. if TP and TQ are the two tangents to a circle with centre O so that ∠POQ = 110°, then ∠PTQ is equal to **

(a) 60°

(b) 70°

(c) 80°

(d) 90°

**Answer**

B

**Fill in the Blanks :**

**Question. There is no tangent to a circle passing through a point lying ………… the circle. **

**Answer**

** inside**

**Question. In given Fig., the length PB = ……………… cm. **

**Answer**

**4 cm**

**Question. The common point of a tangent to a circle and the circle is called ……………… . **

**Answer**

** Point of contact**

**Question. The tangent to a circle is ………….. to the radius through the point of contact. **

**Answer**

**perpendicular**

**Question. The lengths of the two tangents from an external point to a circle are …………. . **

**Answer**

** equal**

**True Or False :**

**Question. If P is a point on a circle with centre C, then the line drawn through P and perpendicular to CP is the tangent to the circle at the point P. **

**Answer**

**True**

**Question. The tangent to a circle is a special case of the secant. **

**Answer**

**True**

**Question. In a circle, two chords PQ and RS bisect each other. Then PRQS is a rectangle. **

**Answer**

**True**

**Question. The centre of the circle lies on the bisector of the angle between the two tangents. **

**Answer**

**True**

**Question. Line joining the centers of two intersecting circles always bisect their common chord. **

**Answer**

**True**

**Match the Following :**

**Question . If AB is a chord of length 6 cm of a circle of radius 5cm, the tangents at A and B intersect at a point X (figure), then match the columns.**

Column-I | Column-II |

(A) AY | (p) 4 cm |

(B) OY | (q) 3.75 cm |

(C) XA | (r) 5 cm |

(D) OA | (s) 3 cm |

**Answer**

(A) → (s); (B) → (p); (C) → (q); (D) → (r)

**Question. If two tangents PA and PB are drawn to a circle with centre O from an external point P (figure), then match the column**

Column-I | Column-II |

(A) ∠ PAB | (p) 90° |

(B) ∠ OAP | (q) q/2 |

(C) ∠ OAB | (r) 90° −θ/2 |

(D) ∠ AOB | 180° – θ |

**Answer**

(A) → (r); (B) → (p); (C) → (q); (D) → (s)

** Question. If an isosceles ΔABC in which AB = AC = 6 cm is inscribed in a circle of radius 9 cm, then. **

Column-I | Column-II |

(A) AP | (p) 8 √2 |

(B) CP | (q) 4 √2 |

(C) OB | (r) 2 |

(D) Area of ΔABC | (s) 9 |

**Answer**

(A) → (r); (B) → (q); (C) → (s); (D) → (p)

** Question. A circle is inscribed in a ΔABC having sides AB = 8 cm, BC = 10 cm and CA = 12 cm as shown in figure. Observe the diagram and match the columns. **

Column-I | Column-II |

(A) AD | (p) 15 |

(B) BE | (q) 7 cm |

(C) CF | (r) 3 cm |

(D) AD + BE + CF | (s) 5 cm |

**Answer**

(A) → (s); (B) → (r); (C) → (q); (D) → (p)

**Question. **

Column-I Definition | Column-II Term |

(A) A line segment which join any two points on a circle. | (p) Secant |

(B) A line which intersect the circle in two points. | (q) Tangent |

(C) A line that intersects the circle at only one point | (r) Chord |

**Answer**

(A) → (r); (B) → (p); (C) → (q)

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