NCERT solution class 10 chapter 10 Circles exercise 10.1 mathematics

EXERCISE 10.1

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Circles Introduction, CBSE Maths Class 10th

Theorem 10.1, "Circles" CBSE Class Xth Mathematics

Page No 209:

Question 1:

How many tangents can a circle have?

Answer:

A circle can have infinite tangents.

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) One
(ii) Secant
(iii) Two
(iv) Point of contact

Q 3, Ex. 10.1, Circles, NCERT Solutions, Class 10th Mathematics

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)  cm test

Answer:

We know that the line drawn from the centre of the circle to the tangent is perpendicular to the tangent.
OP PQ
By applying Pythagoras theorem in ΔOPQ,

OP² + PQ² = OQ² 
5² + PQ² =12² 
PQ² =144 − 25
PQ = cm.
Hence, the correct answer is (D).

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:

It can be observed that AB and CD are two parallel lines. Line AB is intersecting the circle at exactly two points, P and Q. Therefore, line AB is the secant of this circle. Since line CD is intersecting the circle at exactly one point, R, line CD is the tangent to the circle.

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