CBSE Class 10 Circles Sure Shot Questions Set 04

MCQ BASED QUESTIONS 

Question. The common point of a tangent to a circle with the circle is called ___________
(a) Centre
(b) point of contact
(c) end point
(d) None of the options
Answer: (b) point of contact

Question. If radii of two concentric circles are 4 cm and 5 cm, then the length of each chord of one circle which is tangent to the other circle is -----
(a) 3cm
(b) 1cm
(c) 6cm
(d) 9cm
Answer: (d) 9cm

Question. If angle between two radii of a circle is \( 130^\circ \), the angle between the tangents at the ends of the radii is :
(a) \( 90^\circ \)
(b) \( 50^\circ \)
(c) \( 70^\circ \)
(d) \( 40^\circ \)
Answer: (b) \( 50^\circ \)

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) \( \sqrt{119} \) cm.
Answer: (d) \( \sqrt{119} \) cm.

Question. A circle can have _____parallel tangents at a single time.
(a) One
(b) Two
(c) Three
(d) Four
Answer: (b) Two

Question. A line intersecting a circle in two points is called a _______.
(a) Secant
(b) Chord
(c) Diameter
(d) Tangent
Answer: (a) Secant

Question. In the given Fig., AB is a chord of the circle and AOC is its diameter such that \( \angle ACB = 50^\circ \). If AT is the tangent to the circle at the point A, the \( \angle BAT \) is equal to
(a) \( 65^\circ \)
(b) \( 60^\circ \)
(c) \( 40^\circ \)
(d) \( 50^\circ \)
Answer: (d) \( 50^\circ \)

Question. The area of the circle that can be inscribed in a square of each 6cm is
(a) \( 36\pi \) sq.cm
(b) \( 18\pi \) sq.cm
(c) \( 12\pi \) sq.cm
(d) \( 9\pi \) sq.cm
Answer: (d) \( 9\pi \) sq.cm

Question. If two tangents inclined at an angle of \( 60^\circ \) are drawn to a circle of radius 3cm, then the length of each tangent is equal to
(a) \( 3\sqrt{3}/ 2 \) cm
(b) 3cm
(c) 6cm
(d) \( 3\sqrt{3} \) cm
Answer: (d) \( 3\sqrt{3} \) cm

Question. The number of tangents drawn from a point lies inside the circle is --------
(a) Two tangents
(b) only one tangent
(c) No tangents
(d) Infinite tangents
Answer: (c) No tangents

Question. The number of tangents drawn from a point lies on the circle is --------
(a) Two tangents
(b) only one tangent
(c) No tangents
(d) Infinite tangents
Answer: (b) only one tangent

Question. The number of tangents drawn from a point lies outside the circle is --------
(a) Two tangents
(b) only one tangent
(c) No tangents
(d) Infinite tangents
Answer: (a) Two tangents

ASSERTION AND REASONING BASED QUESTION

Question. Assertion (A): If in a circle, the radius of the circle is 3 cm and distance of a point from the centre of a circle is 5 cm, then length of the tangent will be 4 cm.
Reason (R): \( (\text{hypotenuse})^2 = (\text{base})^2 + (\text{height})^2 \)
(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
(b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
(c) Assertion (A) is true but reason (R) is false.
(d) Assertion (A) is false but reason (R) is true.
Answer: (a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).

Question. Assertion (A): The two tangents are drawn to a circle from an external point, then they subtend equal angles at the centre.
Reason (R): A parallelogram circumscribing a circle is a rhombus.
(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
(b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
(c) Assertion (A) is true but reason (R) is false.
(d) Assertion (A) is false but reason (R) is true.
Answer: (b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).

Question. Assertion (A): PA and PB are two tangents to a circle with centre O. Such that \( \angle AOB = 110^\circ \), then \( \angle APB = 90^\circ \).
Reason (R): The length of two tangents drawn from an external point are equal.
(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
(b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
(c) Assertion (A) is true but reason (R) is false.
(d) Assertion (A) is false but reason (R) is true.
Answer: (d) Assertion (A) is false but reason (R) is true.

Question. Assertion (A): The length of the tangent drawn from a point 8cm away from the centre of circle of radius 6cm is \( 2\sqrt{7} \) cm.
Reason (R): If the angle between two radii of a circle is \( 130^\circ \), then the angle between the tangents at the end points of radii at their point of intersection is \( 50^\circ \).
(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
(b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
(c) Assertion (A) is true but reason (R) is false.
(d) Assertion (A) is false but reason (R) is true.
Answer: (b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).

Question. Assertion (A): If a chord AB subtends an angle of \( 60^\circ \) at the centre of a circle, then the angle between the tangents at A and B is also \( 60^\circ \).
Reason (R): The length of the tangent from an external points P on a circle with centre O is always less than OP.
(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
(b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
(c) Assertion (A) is true but reason (R) is false.
(d) Assertion (A) is false but reason (R) is true.
Answer: (d) Assertion (A) is false but reason (R) is true.