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Ex 10.2, 6 - The length of a tangent from a point A at - Theorem 10.1: Tangent perpendicular to radius (numerical type)

  1. Chapter 10 Class 10 Circles
  2. Serial order wise
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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, Δ 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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  • Harshita Singh's image
    It is given that the length of a tangent from point A is 5cm from the centre of their circle is 4 cm .... So how come AB is 4 cm and OA  is 5cm .
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