Question

If a pair of tangents to a circle of 5cm is Inclined at a angle of 90° find length of tangent

Answer 1

Answer:

Step-by-step explanation:

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.