Class 10, Maths, Chapter 10, Exercise 10.1 Solutions
Q.1. How many tangents can a circle have?
Ans: A circle can have an infinite number of tangents.
Q.2. Fill in the blanks:
(i) A tangent to a circle intersects it in………………….. point (s).
(ii) A line intersecting a circle in two points is called a ………………………
(iii) A circle can have ………………………parallel tangents at the most.
(iv) The common point of a tangent to a circle and the circle is called ………………
Ans: (i) only one
(ii) secant
(iii) two
(iv) point of contact
(See Answer below)
Q.3. 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) $\sqrt{119}\,\,cm$
Ans: (D)
Q.4. 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.
Ans: Here ‘a’ is the given line and a circle with centre O is drawn.
Line PT is drawn || to line ‘a’.
PT is the tangent to the circle.
AB is drawn || to line ‘a’ and is the secant.