Ex 10.2, 6 - The length of a tangent from a point A at - Ex 10.2

Ex 10.2, 6 - Chapter 10 Class 10 Circles - Part 2

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Ex 10.2,6 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. Given: Let the circle be with centre O AB is the tangent from point A Length of tangent = AB = 4cm Also, distance of point from circle = 5 cm Hence OA = 5cm To find: Radius i.e. OB Solution: Since AB is tangent Hence OB AB OBA = 90 So, OAB is a right triangle In right triangle OAB Using Pythagoras theorem (Hypotenuse)2 = (Height)2 + (Base)2 OA2 = OB2 + AB2 52 = OB2 + 42 OB2 = 25 16 OB2 = 9 OB = 9 OB = (3^2 ) OB = 3 Hence, radius of the circle = OB = 3cm

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo