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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? 
 

 May 18, 2020
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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!

 May 18, 2020

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