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
Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.
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