DS Geometry question

[falu09]

Circle c and line k lie in the xy-plane. If Circle c is centered at the origin and has a radius of 1, does line k intersect circle c?

1. The x-intercept of line k is > 1
2. The slope of line k is -1/10

Please explain how to solve.

[ak7]

I think it's E.

Sketch the circle.

1) x-intercept is more than 1, so outside of the circle. Take a couple of examples to see if it "must" cross or "must not" cross, vs. "could cross or not cross" If slope is very steep and positive, it doesn't cross. For some other slopes, you can easily see that it might cross. So INSUFF.

2) slope of k is -1/10 ... so it's almost flat and negative. If the y-intercept is something like 20, it never crosses. But if the y-intercept is something like 0, then it does. INSUFF.

1&2) If the x-intercept is something like 2 and the slope is -1/10, then it crosses. however, if the x-intercept is a very large number, something like 200, then the line may go over the circle and never cross. INSUFF.


What is the Official Answer?

[falu09]

Thanks for the great explanation....Official Answer is

SPOILER: E