Let a, b, c be the lengths of sides BC, CA, AB respectively of a triangle ABC. If p is the perimeter and q is the area of the triangle, then what is $p(p-2a) \tan \left(\frac{A}{2}\right)$ equal to ?

A straight line passes through the point of intersection of x + 2y + 2 = 0 and 2x - 3y - 3 = 0. It cuts equal intercepts in the fourth quadrant. What is the sum of the absolute values of the intercepts?

Under which one of the following conditions are the lines ax + by + c = 0 and bx + ay + c = 0 parallel (a ≠ 0, b ≠ 0)?

What is the equation of the locus of the mid-point of the line segment obtained by cutting the line x + y = p, (where p is a real number) by the coordinate axes ?