1994 AMC 12 Problem 4

Attempt Problem 4 of the 1994 AMC 12 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1994 AMC 12 solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

In the

xy

-plane, the segment with endpoints

(-5,0)

and

(25,0)

is the diameter of a circle. If the point

(x,15)

is on the circle, then

x=

10

12.5

15

17.5

20

Find the center and radius from the diameter endpoints

The point’s vertical distance from the center already equals the radius

The center is

(10,0)

and the radius is

15.

Thus

(x-10)^2+15^2=15^2,

x=10.

Thus the correct answer is A.

Problem 4 in other years