2023 AMC 12B Problem 10


In the xyxy -plane, a circle of radius 44 with center on the positive xx -axis is tangent to the yy -axis at the origin, and a circle with radius 1010 with center on the positive yy -axis is tangent to the xx -axis at the origin. What is the slope of the line passing through the two points at which these circles intersect?

(A) 27(B) 37(C) 229(D) 129(E) 25\textbf{(A)}\ \dfrac{2}{7} \qquad\textbf{(B)}\ \dfrac{3}{7} \qquad\textbf{(C)}\ \dfrac{2}{\sqrt{29}} \qquad\textbf{(D)}\ \dfrac{1}{\sqrt{29}} \qquad\textbf{(E)}\ \dfrac{2}{5}


Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.

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Category: AMC 12B
Points: 2
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