If two tangents are inclined at 60° are drawn to a circle of radius 3 cm then find length of each tangent.
CBSE Class 10 Sample Paper for 2021 Boards - Maths Standard
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CBSE Class 10 Sample Paper for 2021 Boards - Maths Standard
Last updated at April 16, 2024 by Teachoo
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