Skip to main content
OlympiadHQ

Browse · harp

Print

smc

geometry senior

Problem

In the -plane, a circle of radius with center on the positive -axis is tangent to the -axis at the origin, and a circle with radius with center on the positive -axis is tangent to the -axis at the origin. What is the slope of the line passing through the two points at which these circles intersect?
(A)
(B)
(C)
(D)
(E)
Solution
The center of the first circle is . The center of the second circle is . Thus, the slope of the line that passes through these two centers is . Because this line is the perpendicular bisector of the line that passes through two intersecting points of two circles, the slope of the latter line is .
Final answer
E