SOLUTION: In the figure above, OP Is a radius of the circle, PX is a tangent of the circle at point P, and the area of triangle OPX is 12. What is the area of the circle? a. 16Pi b. 12P

Algebra ->  Polygons -> SOLUTION: In the figure above, OP Is a radius of the circle, PX is a tangent of the circle at point P, and the area of triangle OPX is 12. What is the area of the circle? a. 16Pi b. 12P      Log On


   

Question 983226: In the figure above, OP Is a radius of the circle, PX is a tangent of the circle at point P, and the area of triangle OPX is 12. What is the area of the circle?
a. 16Pi
b. 12Pi
c. 18Pi
d. 24Pi
Link to image
http://152.46.13.240/MoodleContent/SATprep/Math%20Unit%207/Lesson%203%20Assignment/cb2.gif
Answer by ikleyn(53751) About Me  (Show Source):
You can put this solution on YOUR website!

The triangle  OPX  is right-angled triangle because the radius drawn to the tangent point is perpendicular to the tangent.
Therefore the area of the triangle  OPX  is half-product of its legs  OP  and  PX:

S = 12 = 1%2F2.|OP|.|OP| = 1%2F2*|OP|*6 = 3*|OP|.

It gives for the radius of the circle   r = |OP| = 12%2F3 = 4.

Hence,  the area of the circle is  pi%2Ar%5E2 = pi%2A4%5E2 = 16pi.

Answer.  The area of the circle is  16pi.