Prove that the length of the common chord of the two circles : (x - a)^2 + (y - b)^2…

MATHEMATICS · Subjective · CBSE · Mathematics · Conic Sections · Conic Sections

Problem

Prove that the length of the common chord of the two circles : (x−a)2+(y−b)2=c2(x - a)^2 + (y - b)^2 = c^2 and (x−b)2+(y−a)2=c2 is 4c2−2(a−b)2.\text{and } (x - b)^2 + (y - a)^2 = c^2 \text{ is } \sqrt{4c^2 - 2(a - b)^2}. Find also the condition when the given circles touch.

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