RD Sharma Solutions Chapter 10 Circles Exercise 10.1 Class 10 Maths

RD Sharma Solutions Chapter 10 Circles Exercise 10.1 Class 10 Maths

Chapter Name

RD Sharma Chapter 10 Circles

Book Name

RD Sharma Mathematics for Class 10

Other Exercises

  • Exercise 10.2

Related Study

NCERT Solutions for Class 10 Maths

Exercise 10.1 Solutions

1. Fill in the blanks 
(i) The common point of tangent and the circle is called point of contact. 
(ii) A circle may have two parallel tangents. 
(iii) A tangent to a circle intersects it in one point. 
(iv) A line intersecting a circle in two points A called a secant. 
(v)  The angle between tangent at a point P on circle and radius through the point is 90° . 


2. How many tangents can a circle have ? 


Tangent: A line intersecting circle in one point is called a tangent. 

As there are infinite number of points on the circle a circle has many (infinite) tangents. 

3. O is the center 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


Consider a circle with center O and radius OA = 8 cm = r, AB = 15 cm

(AB) tangent is drawn at A(point of contact)
At point of contact, we know that radius and tangent are perpendicular. 
In ΔOAB, ∠OAB = 90°, By Pythagoras theorem 

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


PQ = 24 cm 
OQ = 25 cm  
OP = radius = ? 

P is point of contact, At point of contact, tangent and radius are perpendicular to each other 
∴ΔPOQ is right angled triangle ∠OPQ = 90° 
By Pythagoras theorem, 

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