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In figure, AB is a chord of circle C1 which is a tangent to C2.
Since, tangent is perpendicular to radius through point of contact.
Therefore, Angle OCA is 90° => OA = a, OC= b
In triangle OCA, OA²= OC²+AC²
=> a² = b²+AC² => AC = √a²-b²
Therefore, length of the chord AB = 2AC = 2√a²-b²
Hope you understand
If it is wrong, sorry
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