Question

PLEASE HELP!! Step by step if possible

Answer 1

r = 9

Explanation:

`In\: \odot O,` QP is tangent at point P and OP is radius.

`\therefore OP\perp QP`

`\therefore m\angle OPQ = 90\degree`

So,
`\triangle OPQ` is a right angled triangle. Hence, OQ will be its HYPOTENUSE such that OQ = r + 32

Now, by Pythagoras theorem:

`OQ^2 = OP^2 + PQ^2`

`\therefore (r + 32)^2 = r^2 + (40)^2`

`\therefore\cancel {r^2} + 64r + 1024 = \cancel {r^2} + 1600`

`\therefore 64r = 1600-1024`

`\therefore 64r = 576`

`\therefore r = (576)/(64)`

`\therefore r = 9`