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Question
If two tangents inclined at an angle of 60° are drawn to a circle of radius 3 cm the length of each tangent is equal to ______
Options
`(3sqrt(3))/2 ` cm
6 cm
3 cm
`3sqrt(3)` cm
Solution
If two tangents inclined at an angle of 60° are drawn to a circle of radius 3 cm the length of each tangent is equal to `underlinebb(3sqrt(3) cm)`.
Explanation:
Let P be an external point from which pair of tangents are drawn as shown in the figure given below:
Join OA and OP
Also, OP is a bisector line of ∠APC.
∠APO = ∠CPO = 30°
OA ⊥ AP
Therefore, in triangle OAP
tan 30° = `"OA"/"AP"`
`1/sqrt3 = 3/"AP"`
AP = `3sqrt3` cm
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