Ex 10.5, 2 - A chord of a circle is equal to radius - Ex 10.5

Ex 10.5, 2 - Chapter 10 Class 9 Circles - Part 2

 

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Transcript

Ex 9.3, 2 A chord of a circle is equal to the radius of the circle. Find the angle subtended by the chord at a point on the minor arc and also at a point on the major arc. Given: A circle with chord AB AB = Radius of circle Let point C be a point on the minor arc & point D be a point on the major arc To find: Angle subtended by chord at a point in the minor arc, i.e. , ∠ACB & Angle subtended by chord at a point in the major arc, i.e. , ∠ADB Construction: Join OA & OB Explanation: In ΔOAB, AB = OA = OB = radius ∴ ΔOAB is an equilateral triangle. ⇒ ∠AOB = 60° Arc ADB makes ∠ AOB at centre & angle ∠ ADB at point D So, ∠AOB = 2∠ADB 60° = 2∠ADB 2∠ADB = 60° ∠ADB = 1/2 × (60°) = 30° Also, ADBC forms a cyclic quadrilateral So, ∠ADB + ∠ACB = 180° 30° + ∠ACB = 180° ∠ACB = 180° – 30° ∠ACB = 150°

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.