Question 18 (OR 1st question) - CBSE Class 10 Sample Paper for 2020 Boards - Maths Standard - Solutions of Sample Papers for Class 10 Boards

Last updated at April 16, 2024 by Teachoo

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.

If the angle between two tangents drawn from an external point ‘P’ to

Question 18 (OR 1st question) - CBSE Class 10 Sample Paper for 2020 Boards - Maths Standard - Part 2

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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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.

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