Tamil Nadu Board of Secondary EducationSSLC (English Medium) Class 10th
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A tangent ST to a circle touches it at B. AB is a chord such that ∠ABT = 65°. Find ∠AOB, where “O” is the centre of the circle. - Mathematics

Sum

A tangent ST to a circle touches it at B. AB is a chord such that ∠ABT = 65°. Find ∠AOB, where “O” is the centre of the circle.

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Solution

Given ∠ABT = 65°

∠OBT = 90°  ...(TB is the tangent of the circle)

∠ABO = 90° – 65° = 25°

∠ABO + ∠BOA + ∠OAB = 180°

25° + x + 25° = 180° ...(Sum of the angles of a ∆)

OA and OB are the radius of the circle.

∴ ∠ABO = ∠BAO = 25°

x + 50 = 180°

x = 180° – 50° = 130°

∴ ∠BOA = 130°

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APPEARS IN

Samacheer Kalvi Mathematics Class 10 SSLC Tamil Nadu State Board
Chapter 4 Geometry
Exercise 4.4 | Q 5 | Page 198
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