Question

Find the length of a tangent drawn to a circle with radius 5 cm, from a point 13 cm from the centre of the circle.

Answer 1

Figure..

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Answer 2

To Find the Length of the Tangent is XP and can be calculated using the right angled triangle formula.

Explanation:

Here we have O = center of the circle.

 P = point (outside the circle)

 OP = 13 cm (given).

 OX = 5 cm (given - radius of the circle).

 <POX =90˚ (tangent to the circle touches the circle at x and xo is the radius, forms an angle 90˚).

So as per the given angle ∆ PXO = right angled triangle.

Thus, PX2 + OX2 = PO2.

Or, PX2 = PO2 – OX2.   (by Pythagorean theorem for right angled triangle).

      PX2 = 132 - 52

      PX2 = 169 – 25

 PX2 = 144

 PX = √ 144

 PX = 12 cm.