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Coaxial System

The lengths o...

Question

The lengths of tangents from a fixed point to three circles of coaxial system are $t_{1}, t_{2}, t_{3}$ and if P, Q and R be the centres, then $Q R t_{1}^{2} + R P t_{2}^{2} + P Q t_{3}^{2}$ is equal to

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Solution

The correct option is D \N
Co-axial system $x^{2} + y^{2} + 2 g x + c = 0$ , (g variable)
$L . H . S = Σ (g_{2} - g_{3}) (h^{2} + k^{2} - c + 2 g_{1} h) = 0$
$Σ (g_{2} - g_{3}) = 0 a n d Σ g_{1} (g_{2} - g_{3}) = 0$ .

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