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
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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) (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 = .|OP|.|OP| = *|OP|* = 3*|OP|.
It gives for the radius of the circle r = |OP| = = 4.
Hence, the area of the circle is = = .
Answer. The area of the circle is .
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