If two tangents inclined at an angle of 60 are drawn to circle of radius 13cm , then length of each tangent is equal to:

Let PA and PB be two tangents to a circle with centre O and radius 13 cm.

We are given ∠APB = 60°

We know that two tangents drawn to a circle from an external point are equally inclined to the segment joining the centre to the point.

∴ ∠APO = ∠BPO = × ∠APB = × 60° = 30°

Also, OA ⊥ AP and OB ⊥ BP (radius  ⊥ tangent at point of contact)

In right ΔOAP,

∴ PA = PB =  (Lengths of tangents drawn from an external point to the circle are equal)

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13 root 3. By applying trigonometry in the right triangle with angle 30 degree and the one side as 13 m.

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