NCERT Class 10 Maths Chapter 10 Circles Solutions Video Lessons
#1
Online video classes by CBSE class 10 Maths expert Radhika Polina. In these classes teacher will help you to understand the important theories of the Chapter Circles and to solve all the problems in Chapter 10 Circles in CBSE class 10 text book

PART 1- Introduction to Circles

Teacher introduces the chapter circles and explains the important concepts in the chapter
like Circle, Radius, Chord, Diameter, Segment, Arc etc.

Teacher also explains the following problems Exercises 10.1

1. How many tangents can a circle have?
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 _________ .

3. A tangent PQ at a point P of a circle of radius 5 cm5 cm meets a line through the center OO at a point Q so that Q=12 cm.Q=12 cm. Length PQ is:

(A) 12 cm  
(B) 13 cm      
©Â 8.5 cm    
(D) √119cm.


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.

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#2
NCERT Class 10 Maths Video Lessons and exercise solutions

Circles| Part-2| Explanation to theorem 10.1 and 10.2

Theorem 10.1 : The tangent at any point of a circle is perpendicular to the radius through the point of contact.

Theorem 10.2 : The lengths of tangents drawn from an external point to a circle are equal.


For the explanation of these theorems and proof

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#3
NCERT Class 10 Maths Video Lessons and exercise solutions


Circles | Part-3| Solutions to Exercise 10.2 Problems(1 to 5)

10.2.1 From a point Q, the length of the tangent to a circle is 24 cm and the distance of Q from the center is 25 cm.
The radius of the circle is
(A)    7 cm 
(B)     12 cm
©Â     15 cm
(D)     24.5 cm

10.2.2  In the given figure, if TP and TQ are the two tangents to a circle with centre Oso that ∠POQ=110∘∠POQ=110∘, then ∠PTQis equal to
(A)60∘
(B)70∘ 
©80∘
(D)90∘


10.2.3 If tangents PA and PB from a point P to a circle with center O are inclined to each other at angle of 80∘,80∘, then ∠POA is equal to
(A)50∘  
(B)60∘   
©70∘    
(D)80∘

10.2.4 Prove that the tangents drawn at the ends of a diameter of a circle are parallel.


10.2.5 Prove that the perpendicular at the point of contact to the tangent to a circle passes through the center.

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#4
NCERT Class 10 Maths Video Lessons and exercise solutions


Circles | Part-4| Solutions to Exercise 10.2 Problems(6,7 & 8)

10.2.6 The length of a tangent from a point A at distance 5 cm from the center of the circle is 4 cm. Find the radius of the circle.

10.2.7 Two concentric circles are of radii 5 cm and 3 cm. Find the length of the chord of the larger circle which touches the smaller circle.

10.2.8 A quadrilateral ABCD is drawn to circumscribe a circle (see given Figure). Prove that: AB+CD=AD+BC

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#5
NCERT Class 10 Maths Video Lessons and exercise solutions


Circles | Part-5| Solutions to Exercise 10.2 Problems(9, 10 &11)

10.2.9 In Figure, XY and X′Y′ are two parallel tangents to a circle with center O and another tangent AB with point of contact C intersecting XYat A and X′Y′ at B.

Prove that ∠AOB=90∘

10.2.10 Prove that the angle between the two tangents drawn from an external point to a circle is supplementary to the angle subtended by the line-segment joining the points of contact at the center.


10.2.11 Prove that the parallelogram circumscribing a circle is a rhombus.

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#6
NCERT Class 10 Maths Video Lessons and exercise solutions

Circles | Part-6| Solutions to Exercise 10.2 Problems(12&13)

10.2.12 A triangle ABC is drawn to circumscribe a circle of radius 4cm such that the segments BD and DC into which BCs divided by the point of contact D are of lengths 8cmand 6cm respectively (see Figure). Find the sides AB and AC.


10.2.13 Prove that opposite sides of a quadrilateral circumscribing a circle subtend supplementary angles at the center of the circle.

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