1 Answer

RicardoPons · Answer 1 · 2022-02-19T08:41:58+0000

Answer:

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

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

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

$\therefore 64r = 1600-1024$

$\therefore 64r = 576$

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

$\therefore r = 9$

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