## 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 Oct. 9, 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 OA = OB ∠ OAP = ∠ OBP OP = OP ∴ Δ OPA ≅ Δ OPB (Both Radius) (Both 90°, as radius is perpendicular to tangent) (Common) (SAS Congruency) ∴ ∠ 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 (CPCT)

CBSE Class 10 Sample Paper for 2020 Boards - Maths Standard

Paper Summary

Question 1 Important

Question 2 Important

Question 3

Question 4 Important

Question 5 Important

Question 6 Important

Question 7

Question 8 Important

Question 9 Important

Question 10

Question 11

Question 12 (OR 1st question)

Question 12 (OR 2nd question)

Question 13 Important

Question 14 Important

Question 15 Important

Question 16

Question 17 Important

Question 18 (OR 1st question) Important You are here

Question 18 (OR 2nd question) Important

Question 19

Question 20

Question 21 Important

Question 22 Important

Question 23 (OR 1st question) Important

Question 23 (OR 2nd question)

Question 24 Important

Question 25 (OR 1st question) Important

Question 25 (OR 2nd question)

Question 26 Important

Question 27 (OR 1st question)

Question 27 (OR 2nd question) Important

Question 28 Important

Question 29 (OR 1st question)

Question 29 (OR 2nd question)

Question 30 Important

Question 31 Important

Question 32 (OR 1st question) Important

Question 32 (OR 2nd question) Important

Question 33 Important

Question 34 Important

Question 35 (OR 1st question) Important

Question 35 (OR 2nd question)

Question 36

Question 37 (OR 1st question)

Question 37 (OR 2nd question)

Question 38 (OR 1st question)

Question 38 (OR 2nd question) Important

Question 39

Question 40 Important

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.