The center of a circle is C(2α - 1, 3α + 1) and it passes through the point A(-3, -1). If a diameter of the circle is of length 20 units, find the value(s) of α.

Check whether the points (5, -2), (6, 4) and (7, -2) are the vertices of an isosceles triangle.

Using distance formula, show that (3, 3) is the center of the circle passing through the points (6, 2), (0, 4) and (4, 6).

Name the type of triangle formed by the points A(-5, 6), B(-4, -2) and C(7, 5).