Question

Length of a tangent segment drawn from a point which is at a distance 13 cm from the centre of a circle is 12 cm, find the diameter of the circle.​

Answer 1

Step-by-step explanation:

Using Pythagoras theorem

$= \geqslant ab {}^{2} + {ob}^{2} = {ao}^{2} \\ = > {12}^{2} + {ob}^{2} = {13}^{2} \\ = > {ob}^{2} = {13}^{2} - {12}^{2} \\ = > {ob}^{2} = 169 - 144 \\ = > {ob}^{2} = 25 \\ = > ob = 5$

As length cannot be negative

$= > ob \: = 5cm$

Hence length of radius is 5 cm.