In rhombus ABCD, A(7, 3) and C(0, -4) are two opposite vertices. Find :

(i) mid-point of diagonal AC

(ii) mid-point of diagonal BD

(iii) slope of diagonal AC

(iv) the equation of diagonal BD.

From a boat, 300 m away from a vertical pillar, the angles of elevation of the top and the foot of a vertical pillar at the edge of the cliff are 55°40' and 54°20' respectively. Find the height of the pillar correct to the nearest metre.

In the given figure, O and O' are centers of two circles, touching each other at point P. The common tangent at P meets a direct common tangent AB at M. Show that :

(i) M is mid-point of AB.

(ii) ∠APB = 90°

AB is a line segment joining the points A(3, 2) and B(4, 1). Find :

(i) the ratio in which AB is divided by point P on x-axis

(ii) the co-ordinates of point P

(iii) the equation of the line that passes through the point P and is perpendicular to AB.