Two circles with radii $R$ and $r$ intersect at $C$ and $D$ and are tangent to a line $\ell$ at $A$ and $B$. Prove that the circumradius of triangle $ABC$ does not depend on the length of segment $AB$.
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Tags: geometry, circumcircle
Two circles with radii $R$ and $r$ intersect at $C$ and $D$ and are tangent to a line $\ell$ at $A$ and $B$. Prove that the circumradius of triangle $ABC$ does not depend on the length of segment $AB$.