Point P (2, -7) is the centre of a circle with radius 13 units, PT is perpendicular to chord AB and T = (-2, -4); Calculate the length of :

(i) AT

(ii) AB.

Calculate the distance between the points P(2, 2) and Q(5, 4) correct to three significant figures.

Calculate the distance between A(5, -3) and B on the y-axis whose ordinate is 9.

Find the point on y-axis whose distances from the points A(6, 7) and B(4, -3) are in the ratio 1 : 2.