Class 10 RD Sharma Solutions – Chapter 10 Circles – Exercise 10.1

Question 1. Fill in the blanks :

(i) The common point of a tangent and the circle is called ……….

Solution:

Point of contact.

(ii) A circle may have ………. parallel tangents.

Solution:

 Two 

(iii) A tangent to a circle intersects it in ……….. point(s).

Solution:

One

(iv) A line intersecting a circle in two points is called a …………

Solution:

Secant

(v) The angle between tangent at a point on a circle and the radius through the point is ………..

Solution:

Right angle (90°)

Question 2. How many tangents can a circle have?

Solution:

Tangent is a line that intersect a circle at only point. Since there are a infinite number of points on a circle, a circle can have infinite tangents.

Question 3. O is the centre of a circle of radius 8 cm. The tangent at a point A on the circle cuts a line through O at B such that AB = 15 cm. Find OB.

Solution:

Radius OA = 8 cm

AB = 15 cm

OA ⊥ tangent AB

Therefore, In right ∆OAB, by applying Pythagoras Theorem:

      OB² = OA² + AB² 

=> OB² = (8)² + (15)² 

            = 64 + 225 = 289 = (17)²

=> OB = 17 cm

Thus, OB = 17 cm

Question 4. If the tangent at a point P to a circle with centre O cuts a line through O at Q such that PQ = 24 cm and OQ = 25 cm. Find the radius of the circle.

Solution:

OP is the radius

OQ = 25 cm

PQ = 24 cm

OP ⊥ tangent PQ

therefore, In right ∆OPQ, by applying Pythagoras Theorem:

      OQ² = OP² + PQ² 

=> (25)² = OP² + (24)²

=> 625 = OP² + 576

=> OP² = 625 – 576 = 49

=> OP² = (7)²

     OP = 7 cm

Thus, radius of the circle is 7 cm

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