Class 10 Maths Chapter – 10 Circle EXERCISE 10.1 Questions and Answers
EXERCISE 10.1
Q1. How many tangents can a circle have?
Answer: A circle can have infinitely many tangents, because a tangent can be drawn at every point on the circle, and a circle has infinitely many points.
Q2. Fill in the blanks:
(i) A tangent to a circle intersects it in exactly one point (s).
(ii) A line intersecting a circle in two points is called a secant.
(iii) A circle can have two parallel tangents at the most.
(iv) The common point of a tangent to a circle and the circle is called the point of contact.
Q3. 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) √119 cm.
Given: Radius OP = 5 cm, OQ = 12 cm, PQ is a tangent at P.
To Prove/Find: PQ. Proof: By Theorem 10.1, OP ⊥ PQ, so ∠OPQ = 90°.
In right triangle OPQ:
Q4. Draw a circle and two lines parallel to a given line such that one is a tangent and the other, a secant to the circle.
Answer: (construction steps):
- Draw a circle with centre O.
- Draw any line l, and draw two lines parallel to l that cut the circle.
- Shift one parallel line until it touches the circle at exactly one point — this is the tangent.
- Keep the other parallel line cutting the circle at two points — this is the secant.
