In this page we have *NCERT Solutions for Class 10 Maths Chapter 10:Circle* for
EXERCISE 1 . Hope you like them and do not forget to like , social share
and comment at the end of the page.

- The tangent to a circle is a special case of the secant, when the two end points of its corresponding chord coincide.
- The common point of the tangent and the circle is called the point of contact
- The tangent at any point of a circle is perpendicular to the radius through the point of contact

How many tangents can a circle have?

A circle can have infinite tangents.

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 ............

(i) one

(ii) secant

(iii) two

(iv) point of contact

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

We know that the line drawn from the centre of the circle to the tangent is perpendicular to the tangent.

So OP ⊥ PQ

Now By Pythagoras theorem in ΔOPQ,

OQ

(12)

PQ

PQ = √119 cm

(D) is the correct option.

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.

AB and XY are two parallel lines where AB is the tangent to the circle at point C while XY is the secant to the circle.

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