4.05: Two circles and common chord

0606/22/M/J/26 — Question 11 · 9 marks

Circle \(C_1\) has centre \((3,5)\) and passes through \(P=(1,4)\). Circle \(C_2\) has centre \((12,8)\). Their common chord has equation \(y=19-3x\).
Find the radius of \(C_2\).
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