### 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.

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