In the diagram below of *PAO*, *AP* is tangent to circle *O* at point *A*, *OB* = 7, and *BP* = 18.

What is the measure of line segment OA?

What is the measure of line segment OP?

What is the measure of line segment AP?

GAMEMASTERX40 May 18, 2020

#1**+3 **

Since OB is also the radius, and is 7, the radius is 7, so OA is also the length of radius. \(\overline{OA} = 7\).

\(\overline{OP} = \overline{OB} + \overline{BP} = 7 + 18 = 25.\)

Lastly since \(\triangle OAP\) is probably right, so.. using the pythogoream theroem, the hypothenuse \(\overline{OP}^2 = \overline{OA} ^2 + \overline{AP}^2 = 25^2 = 7^2 + \overline{AP}^2 \)

Thus,

\(\overline{AP}^2 = 25^2 - 7^2 = 625 - 49 = 576\)

SO \(\overline{AP} = \sqrt{576} = 24\)

So those are your answers!

If you dont' understand anything feel free to ask!

hugomimihu May 18, 2020