Let $$\mathrm{A}(\alpha,-2), \mathrm{B}(\alpha, 6)$$ and $$\mathrm{C}\left(\frac{\alpha}{4},-2\right)$$ be vertices of a $$\triangle \mathrm{ABC}$$. If $$\left(5, \frac{\alpha}{4}\right)$$ is the circumcentre of $$\triangle \mathrm{ABC}$$, then which of the following is NOT correct about $$\triangle \mathrm{ABC}$$?

Let the circumcentre of a triangle with vertices A(a, 3), B(b, 5) and C(a, b), ab > 0 be P(1,1). If the line AP intersects the line BC at the point Q$$\left(k_{1}, k_{2}\right)$$, then $$k_{1}+k_{2}$$ is equal to :

The equations of the sides $$\mathrm{AB}, \mathrm{BC}$$ and CA of a triangle ABC are $$2 x+y=0, x+\mathrm{p} y=39$$ and $$x-y=3$$ respectively and $$\mathrm{P}(2,3)$$ is its circumcentre. Then which of the following is NOT true?

Let $$A(1,1), B(-4,3), C(-2,-5)$$ be vertices of a triangle $$A B C, P$$ be a point on side $$B C$$, and $$\Delta_{1}$$ and $$\Delta_{2}$$ be the areas of triangles $$A P B$$ and $$A B C$$, respectively. If $$\Delta_{1}: \Delta_{2}=4: 7$$, then the area enclosed by the lines $$A P, A C$$ and the $$x$$-axis is :