Question

O is the centre of a circle of radius 8 cm. The tangent at a point A on the circle cuts a line through O at B such that AB=15 cm. Find OB.

Answer 1

Given data : AB = 15 cm

OA = 8 cm ( radius of the circle )

We know that the tangent cuts the circle at ${90}^{\circ }$. Therefore, OA is the hypotenuse of the triangle OAB . Hence, the longest side can be found by using Pythagoras Theorem.

We have,

$O{B}^2=O{A}^2+A{B}^2$

$O{B}^2=64+225$

$O{B}^2=289$

$\therefore OB=17cm$