+0

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

+1
162
1
+956

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

#1
+927
0

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 $$\overline{AP} = \sqrt{576} = 24$$