# 10. Circles

##### 2 LECTURES

• This page has links to complete syllabus of NCERT Chapter 10 Circles based on syllabus recommended by CBSE based on class 10 maths.
• There are 2 video lectures having explanations from basic to advance concepts, each and every NCERT solutions, questions and all important examples. You can access them directly from the lecture menu or just scroll down the page.
• All lecture were uploaded on YouTube so for better learning experience here you will find link to YouTube Playlist of Chapter 10 Circles.
• Also, there are detailed highlights of each video lecture with exact timestamp links so that you can easily access all topics and questions directly.
• Just click on the timestamp link and you will be redirected to video watch page at exactly that time.

## PDFs OF LECTURES

##### 10(A) || Theorem 10.1 NCERT Exercise 10.1

00:00:05 Meaning of Tangent and Secant Through a Circle

00:02:53 Point of Contact of Tangent

00:05:28 Proof of Radius is always Perpendicular to Tangent Theorem 10.1 : The tangent at any point of a circle is perpendicular to the radius through the point of contact.

00:14:02 NCERT Exercise 10.1 Question 1 How many tangents can a circle have?

00:14:52 NCERT Exercise 10.1 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……………….

00:17:12 NCERT Exercise 10.1 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 :

00:20:12 NCERT Exercise 10.1 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.

##### 10(B) || Theorem 10.2 NCERT Exercise 10.2 Q1 to Q6

00:00:17 Theorem 10.2 The lengths of tangents drawn from an external point to a circle are equal.

00:11:27 NCERT Exercise 10.2 Question 1 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 (C) 15 cm (B) 12 cm (D) 24.5 cm

00:14:57 NCERT Exercise 10.2 Question 2 In Fig. 10.11, if TP and TQ are the two tangents to a circle with centre O so that ∠ POQ = 110°, then ∠ PTQ is equal to (A) 60° (C) 80° (B) 70° (D) 90°

00:18:17 NCERT Exercise 10.2 Question 3 If tangents PA and PB from a point P to a circle with centre O are inclined to each other at angle of 80°, then ∠ POA is equal to (A) 50° (C) 70° (B) 60° (D) 80°

00:23:45 NCERT Exercise 10.2 Question 4 Prove that the tangents drawn at the ends of a diameter of a circle are parallel.

00:28:17 NCERT Exercise 10.2 Question 5 Prove that the perpendicular at the point of contact to the tangent to a circle passes through the centre.

00:35:17 NCERT Exercise 10.2 Question 6 The length of a tangent from a point A at distance 5 cm from the centre of the circle is 4 cm. Find the radius of the circle.

##### 10(C) || NCERT Exercise 10.2 Q7 to Q13

00:00:05 NCERT Exercise 10.2 Question 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.

00:09:32 NCERT Exercise 10.2 Question 8 A quadrilateral ABCD is drawn to circumscribe a circle (see Fig. 10.12). Prove that AB + CD = AD + BC

00:18:02 NCERT Exercise 10.2 Question 11 Prove that the parallelogram circumscribing a circle is a rhombus.

00:28:52 NCERT Exercise 10.2 Question 9 In Fig. 10.13, XY and X′Y′ are two parallel tangents to a circle with centre O and another tangent AB with point of contact C intersecting XY at A and X′Y′ at B. Prove that ∠ AOB = 90°.

00:39:12 NCERT Exercise 10.2 Question 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 centre.

00:45:22 NCERT Exercise 10.2 Question 13 Prove that opposite sides of a quadrilateral circumscribing a circle subtend supplementary angles at the centre of the circle.

##### 10(D) || NCERT Exercise 10.2 Q12 All Examples

00:00:29 Chapter 10 Example 1 Prove that in two concentric circles, the chord of the larger circle, which touches the smaller circle, is bisected at the point of contact.

00:06:10 Chapter 10 Example 2 Two tangents TP and TQ are drawn to a circle with centre O from an external point T. Prove that ∠ PTQ = 2 ∠ OPQ.

00:12:50 Chapter 10 Example 3 PQ is a chord of length 8 cm of a circle of radius 5 cm. The tangents at P and Q intersect at a point T (see Fig. 10.10). Find the length TP.

00:35:58 NCERT Exercise 10.2 Question 12 A triangle ABC is drawn to circumscribe a circle of radius 4 cm such that the segments BD and DC into which BC is divided by the point of contact D are of lengths 8 cm and 6 cm respectively (see Fig. 10.14). Find the sides AB and AC.