If the angle between two tangents drawn from an external point ‘P’ to a circle of radius ‘r’ and centre O is 60° , then find the length of OP.
Last updated at Nov. 1, 2019 by Teachoo
Transcript
Question 18 (OR 1st question) If the angle between two tangents drawn from an external point ‘P’ to a circle of radius ‘r’ and center O is 60° , then find the length of OP. Given that Angle between two tangents is 60° ∴ ∠ APB = 60° Now, In Δ OPA and Δ OPB ∠ OAP = ∠ OBP OP = OP OA = OB ∴ Δ OPA ≅ Δ OPB ∴ ∠ OPA = ∠ OPB So, we can write ∴ ∠ OPA = ∠ OPB = 1/2 ∠ APB So, ∠ OPA = 1/2 × 60° = 30° Now, in Δ OPA sin P = 𝑂𝐴/𝑂𝑃 sin 30° = 𝑟/𝑂𝑃 1/2 = 𝑟/𝑂𝑃 OP = 2r
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CBSE Class 10 Sample Paper for 2020 Boards - Maths Standard
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