P, Q and R are centres and {r₁},,,{r₂},,,{r₃} are radii respectively of three co-axial circles

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10-1.Circle and System of Circles

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$P, Q$ and $R$ are the centres and ${r_1},\,\,{r_2},\,\,{r_3}$ are the radii respectively of three co-axial circles, then $QRr_1^2 + RP\,r_2^2 + PQr_3^2$ is equal to

A

$PQ\;.\,QR\,.\,RP$

B

$ - PQ\,.\,QR\,.\,RP$

C

$P{Q^2}.Q{R^2}.R{P^2}$

D

None of these

Solution

(b) As $\Sigma g_1^2({g_2} – {g_3}) = – ({g_1} – {g_2})({g_2} – {g_3})({g_3} – {g_1})$.

Standard 11

Mathematics

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