Class 10 - Mathematics
Circles - Exercise 10.1
Top Block 1
Exercise 10.1
Question : 1:How many tangents can a circle have?
Answer :
A circle can have infinite number of tangents because a circle can have infinite number of points on it and at every point,
a tangent can be drawn.
Question : 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 ________.
Answer :
(i) A tangent to a circle intersects it in 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 point of contact.
Question : 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) √119 cm.
Answer :
In ΔOPQ, P is right angle. [Since radius is Ʇ to tangent]
OQ2 = PQ2 + OP2
⇒ 122 = PQ2 + 52
⇒ 144 = PQ2 + 25
⇒ PQ2 = 144 – 25
⇒ PQ2 = 119
⇒ PQ = √119
Hence, the option D is the right answer.
Question : 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.
Answer :
Consider a circle with centre O. Let AB is the given line.
Mddle block 1
parallel to AB and passing through X and Y. So, CD and EF are the required lines.
