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# Circles and with radii and , respectively, intersect at distinct points and . A third circle is externally tangent to both and .

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Circles $$\omega_1$$and $$\omega_2$$with radii $$961$$ and $$625$$, respectively, intersect at distinct points $$A$$ and $$B$$. A third circle $$\omega$$is externally tangent to both $$\omega_1$$and $$omega_2$$. Suppose line $$AB$$ intersects $$\omega$$ at two points $$P$$ and $$Q$$ such that the measure of minor arc $$\widehat{PQ}$$ is $$120^{\circ}$$. Find the distance between the centers of $$\omega_1$$ and $$\omega_2$$.

Apr 15, 2021

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The distance between ω1 and ω2 seems to be identical to the length of a radius of a circle ω2.

The ratio of ab:bc must be 1:3      (The length of ac is irrelevant)

Apr 15, 2021
edited by civonamzuk  Apr 15, 2021