Mathematics
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°
Related Questions
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.
Solve the following inequation, write down the solution set and represent it on the real number line. -2 + 10x ≤ 13x + 10 < 24 + 10x, x ∈ R.
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.