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Printjmc
geometry senior
Problem
A circle with a radius of 2 units has its center at . A circle with a radius of 7 units has its center at . A line tangent to both circles intersects the -axis at to the right of the origin. What is the value of ? Express your answer as a common fraction.
Solution
To begin, we can draw a diagram as shown: By drawing in radii to the tangent line, we have formed two right triangles, one with hypotenuse and the other with hypotenuse . Notice that the angles at the axis are vertical angles and are also congruent. So, these two triangles are similar, and we can set up a ratio:
Final answer
\frac{10}{3}