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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

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