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Total Questions :17
Exercise 10.1

How many tangents can a circle have?

A circle can have infinite tangents.

Exercise 10.1

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

Exercise 10.1

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

The line drawn from the centre of the circle to the tangent is perpendicular to the tangent.
∴ OP ⊥ PQ

By Pythagoras theorem in ΔOPQ,

OQ2 = OP2 + PQ2
⇒ (12)2 = 52 + PQ2

⇒PQ2 = 144 - 25

⇒PQ2 = 119

⇒PQ = √119 cm

(D) is the correct option.

Exercise 10.1

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.

Exercise 10.2

choose the correct option and give justification.

From a point Q, the length of the tangent to a circle is 24 cm and the distance of Q from the centre is 25 cm. The radius of the circle is

(A)  7 cm
(B) 12 cm
(C) 15 cm
(D) 24.5 cm

The line drawn from the centre of the circle to the tangent is perpendicular to the tangent.

∴ OP ⊥ PQ
also, ΔOPQ is right angled.
OQ = 25 cm and PQ = 24 cm (Given)

By Pythagoras theorem in ΔOPQ,

OQ2 = OP2 + PQ2
⇒ (25)2 = OP2 + (24)2

⇒ OP2 = 625 - 576

⇒ OP2 = 49

⇒ OP = 7 cm

The radius of the circle is option (A) 7 cm.