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NCERT Solutions for Class 10 Maths Chapter 10:Circle Exercise 1


NCERT Solutions

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.
Points to Remember
  • 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
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

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) √119 cm
Answer

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,
OQ2 = OP2 + PQ2
(12)= 52 + PQ2
PQ2 = 119
PQ = √119 cm
(D) is the correct option.
 
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

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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