There are circle with radius R1 and circle with radius R2. We also know the distance between A and O and that angle AOB = phi. The aim is to calculate distance between B and C.

There are circle with radius R1 and circle with radius R2. We also know the distance between A and O and that angle $AOB=\varphi$. The aim is to calculate distance between B and C.
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Libby Weaver
Step 1
From that, with the given, $\mathrm{\angle }A$ can then be found by sine theorem.
Step 2
In $\mathrm{△}AOC$, since AO, OC and $\mathrm{\angle }A$ are known, apply cosine theorem again to find AC. Result then follows.