Question 11 (Choice 2) Draw a pair of tangents to a circle of radius 6cm which are inclined to each other at an angle of 60°. Also find the length of the tangent.
Steps of construction
Draw a circle of radius 6 cm
Draw horizontal radius OQ
3. Draw angle 120° from point O
Let the ray of angle intersect the circle at point R
Now, draw 90° from point Q
5. Draw 90° from point R
6. Where the two arcs intersect, mark it as point P
∴ PQ and PR are the tangents at an angle of 60°
Finding Length of the tangent
Join PO
∴ ∠ RPO = 30°
In Δ RPO
tan P = 𝑂𝑝𝑝𝑝𝑜𝑠𝑖𝑡𝑒/𝐻𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒
tan 30° = 𝑶𝑹/𝑶𝑷
1/√3 = 6/𝑂𝑃
OP = 6√𝟑 cm
Made by
Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.