# CIRCLES CLASS 10 MATHS

Get Complete Syllabus of Chapter 10 Circles Class 10 Maths :
NCERT Exercise 10.1
NCERT Exercise 10.2
NCERT Chapter 10 Examples

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Subject Language: ENGLISH
Explanation Language: HINDI (HINGLISH)

## Lecture - 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.

## Lecture - 2

• 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.

## Lecture - 3

• 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.

## Lecture - 4

• 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.