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10-1.Circle and System of Circles
normal
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 $QRt_1^2 + RPt_2^2 + PQt_3^2$ is equal to
A
$1$
B
$2$
C
$3$
D
$0$
Solution
(d) Co-axial system ${x^2} + {y^2} + 2gx + c = 0$, ($g$ variable)
$L.H.S.$ = $\Sigma ({g_2} – {g_3})({h^2} + {k^2} – c + 2{g_1}h) = 0$
Since $\Sigma ({g_2} – {g_3}) = 0$
and $\Sigma {g_1}({g_2} – {g_3}) = 0$.
Standard 11
Mathematics