+73 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?
+1009 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!
