If
(x1 – x2)2 + (y1 – y2)2 = a2
(x2 – x3)2 + (y2 – y3)2 = b2
(x3 – x1)2 + (y3 – y1)2 = c2 and
\(4\begin{vmatrix}x_1&y_1&1\\x_2&y_2&1\\x_3&y_3&1\end{vmatrix} = \) λ{λ3 – (λ1 + λ2 + λ3)λ2 + (λ1λ2 + λ2λ3 + λ3λ1)λ – λ1λ2λ3} then
(a) \(\lambda \ge \frac 32(\lambda_1\lambda_2\lambda_3)^{1/3}\)
(b) \(\lambda_1\lambda_2\lambda_3 = 8abc\)
(c) \(\sum\lambda_1\lambda_1 =4\sum ab\)
(d) \(2\lambda = \lambda_1+\lambda_2+\lambda_3\)
