If two tangents are inclined at 60° are drawn to a circle of radius 3 cm then find length of each tangent.

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Question 9 (Choice - 1) - CBSE Class 10 Sample Paper for 2021 Boards - Maths Standard - Part 2

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Question 9 (Choice - 1) If two tangents are inclined at 60° are drawn to a circle of radius 3 cm then find length of each tangent. Given that Angle between two tangents is 60° ∴ ∠ APB = 60° By symmetry ∴ ∠ OPA = ∠ OPB = 1/2 ∠ APB So, ∠ OPA = 1/2 × 60° = 30° Also, as radius is perpendicular to tangent ∠ OAP = ∠ OBP = 90° Now, in Δ OPA tan P = 𝑶𝑨/𝑨𝑷 tan 30° = 3/𝐴𝑃 1/√3 = 3/𝐴𝑃 AP = 3√𝟑 cm Thus, Length of each tangent is 3√𝟑 cm

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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, Social Science, Physics, Chemistry, Computer Science at Teachoo.