If two tangents inclined at an angle 60degree are drawn to a circle of radius 3 cm, then find the length of each tangent.
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The tangent to any circle is perpendicular to the radius of the circle at point of contact.
Let two Tangents originate from point A and touch the circle with centre O at point B & C
Now ABO is a right triangle with angle A as 30° and angle B as 90°
Given OB = 3 = Radius of circle.
Now OB/AB = tan 30°
=> AB = OB/tan 30°
= 3/(1/√3) = 3√3
Similarly, it can be shown that AC = 3√3
As per properties of tangents/ circles, the length of both tangents AB & AC are equal.
Let two Tangents originate from point A and touch the circle with centre O at point B & C
Now ABO is a right triangle with angle A as 30° and angle B as 90°
Given OB = 3 = Radius of circle.
Now OB/AB = tan 30°
=> AB = OB/tan 30°
= 3/(1/√3) = 3√3
Similarly, it can be shown that AC = 3√3
As per properties of tangents/ circles, the length of both tangents AB & AC are equal.
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