CBSE Class 10 Mathematics Circles MCQs Set D

Question. If OA and OB are radii and PA and PB are tangents to the circle, which of the following is quadrilateral OAPB?
(a) Rectangle
(b) Square
(c) Parallelogram
(d) Kite
Answer: d

 Question. If ∠APO=18° , find ∠AOB.
(a) 24°
(b) 144°
(c) 108°
(d) 1 75°
Answer: b

Question. Two circles of radii 8 cm and 2 cm have direct common tangent of length 10 cm, find the distance between their centres.
(a) 8cm
(b) 10cm
(c) 21 cm
(d) 200 cm
Answer: a

Question. If the four sides of a quadrilateral ABCD are tangential to a circle, which of the following is true?
(a) AC+AD= BD+CD
(b) AB+CD= BC+AD
(c) AB+CD=AC+BD
(d) AC+AD= BC+AB
Answer: b

Question. If the distance between two circles of radii R and r is d, find the length of the direct common tangent.
(a) √d² +(R – r)²
(b) √d² – (R + r)²
(c) √(R + r)2 + d²
(d) √d² – (R – r)²
Answer: d

Question. If AP= 15 cm and the radius is 8 cm, find the distance of P from the centre of the circle.
(a) 12cm
(b) 15cm
(c) 17cm
(d) 20cm
Answer: c

Question. PQ is a chord of a circle .the tangent XR at X on the circle cuts PQ produced at R. If XR =12 cm , PQ = x cm, QR = (x – 2)cm , find x in cm.
(a) 6
(b) 7
(c) 10
(d) 14
Answer: c

Question. What is the number of common tangents that can be drawn to two intersecting circles touching at two points?
(a) 2
(b) 4
(c) 3
(d) 1
Answer: a

Question. Find ∠APBif ∠OPB= 25° .
(a) 50°
(b) 40°
(c) 70°
(d) 25°
Answer: a

Question. A If all the sides of a parallelogram touch a circle, what is the parallelogram?
(a) A rectangle
(b) A rhombus
(c) A square
(d) A trapezium
Answer: b

Question. If an equilateral triangle ABC is inscribed in a circle, which of the following is formed by the tangents at their vertices?
(a) A scalene triangle
(b) An equilateral triangle
(c) An isosceles triangle
(d) A right triangle
Answer: b

Question. If PB = 20 cm and OA = 15 cm, find the shortest distance between the circle and P.
(a) 25 cm
(b) 15 cm
(c) 30cm
(d) 10cm
Answer: d

Question. PT is a tangent and PAB is a secant of the circle meeting the circle at A and B. If PA = 4 cm and AB = 5 cm. What is the length of PT?
(a) 8 cm
(b) 6 cm
(c) 3 cm
(d) 1 cm
Answer: b

Case Based MCQs

Case I : Read the following passage and answer the questions.

Smita always finds it confusing with the concepts of tangent and secant of a circle. But this time she has determined herself to get concepts easier.

Question. Number of tangents that can be drawn to a circle from a point not on it, is
(a) 1
(b) 2
(c) 0
(d) Infinite

Answer: A

Question. Number of secants that can be drawn to a circle from a point on it is
(a) infinite
(b) 1
(c) 2
(d) 0

Answer: A

Question. A line that touches a circle at only one point is called
(a) Secant
(b) Chord
(c) Tangent
(d) Diameter

Answer: C

Case II : Read the following passage and answer the questions.

Theorem on Circles

If a tangent is drawn to a circle from an external point, then the radius at the point of contact is perpendicular to the tangent.

Question. Two concentric circles are of radii 5 cm and 3 cm. Find the length of the chord of the larger circle which touches the smaller circle.
(a) 8 cm
(b) 4 cm
(c) 10 cm
(d) 6 cm

Answer: A

Question. In the given figure, O is the centre of two concentric circles of radii 5 cm and 3 cm. From an external point P tangents PA and PB are drawn to these circles. If PA = 12 cm, then PB =

(a) 2√10 cm
(b) 2√5 cm
(c) 4√10 cm
(d) 4√5 cm

Answer: C

Question. In the given figure, O is the centre of two concentric circles. From an external point P tangents PA and PB are drawn to these circles such that PA = 6 cm and PB = 8 cm. If OP = 10 cm, then AB =

(a) 1 cm
(b) 2 cm
(c) 4 cm
(d) Can’t be determined

Answer: C

Question. The diameter of two concentric circles are 10 cm and 6 cm. AB is a diameter of the bigger circle and BD is the tangent to the smaller circle touching it at D and intersecting the larger circle at P on producing. Find the length of BP.

(a) 4 cm
(b) 16 cm
(c) 10 cm
(d) 8 cm

Answer: D

Question. Two concentric circles are such that the difference between their radii is 4 cm and the length of the chord of the larger circle which touches the smaller circle is 24 cm. Then the radius of the smaller circle is
(a) 16 cm
(b) 20 cm
(c) 18 cm
(d) None of these

Answer: A

Case III : Read the following passage and answer the questions.

Teaching through Play-Way Method

For class 10 students, a teacher planned a game for the revision of chapter circles with some questions written on the board, which are to be answered by the students. For each correct answer, a student will get a reward.

Question. In the given figure, x + y =

(a) 60°
(b) 90°
(c) 120°
(d) 145°

Answer: B

Question. If PA and PB are two tangents drawn to a circle with centre O from P such that ∠PBA = 50°, then ∠OAB =
(a) 50°
(b) 25°
(c) 40°
(d) 130°

Answer: C

Question. In the given figure, PQ and PR are two tangents to the circle, then ∠ROQ =

(a) 30°
(b) 60°
(c) 105°
(d) 150°

Answer: D

Question. In the given figure, AB is a chord of the circle and AOC is its diameter such that ∠ACB = 55°, then ∠BAT =

(a) 35°
(b) 55°
(c) 125°
(d) 110°

Answer: B

Question. In the adjoining figure, if PC is the tangent at A of the circle with ∠PAB = 72° and ∠AOB = 132°, then ∠ABC =

(a) 18°
(b) 30°
(c) 60°
(d) can’t be determined

Answer: B

Assertion & Reasoning Based MCQs

Directions : In these questions, a statement of Assertion is followed by a statement of Reason is given. Choose
the correct answer out of the following choices :
(a) Assertion and Reason both are correct statements and Reason is the correct explanation of Assertion.
(b) Assertion and Reason both are correct statements but Reason is not the correct explanation of Assertion.
(c) Assertion is correct statement but Reason is wrong statement.
(d) Assertion is wrong statement but Reason is correct statement.

Question. Assertion : If TP and TQ are the two tangents to a circle with centre O so that ∠POQ = 123°, then ∠PTQ = 57°.
Reason : The tangent at any point of a circle is perpendicular to the radius through the point of contact.

Answer: A

Question. Assertion : In the given figure, if PQ is a tangent to the circle with centre O, then the value of ∠POQ is 25°.
Reason : If two tangents are drawn to a circle from an external point, then they subtend equal angles at the centre.

Answer: D

Question. Assertion : In the given figure, all the sides of a quadrilateral ABCD touch a circle with centre O. Then, ∠AOB + ∠COD = 180°.
Reason : The opposite sides of a quadrilateral circumscribing a circle does not subtend supplementary angles at the centre of the circle.

Answer: C

Question. Assertion : At a point P of a circle with centre O and radius 12 cm, a tangent PQ of length 16 cm is drawn. Then, OQ = 20 cm.
Reason : The tangent at any point of a circle is perpendicular to the radius through the point of contact.

Answer: A

Question. Assertion : The secant of circle is perpendicular to the radius of the circle.
Reason : A line that intersects the given circle in two points is called a secant.

Answer: D

Question. Assertion : In the given figure, AOB is a diameter of a circle with centre O and AC is a tangent to the circle at A. If ∠BOC = 125°, then ∠ACO = 35°.
Reason : ∠ACO and ∠BOC form a linear pair.

Answer: C

Question. Assertion : The length of tangents drawn from an external point to a circle are not always equal in length.
Reason : The tangent is always perpendicular to the radius through the point of contact.

Answer: D