In the given figure, PA and PB are tangents at the points A and B respectively of a circle with center O. Q and R are points on the circle, if ∠APB = 70°, find :

(i) reflex angle AOB

(ii) ∠AQB

(iii) ∠ARB

In the given figure, the line segment AB meets x-axis at point A and y-axis at point B.

The point P(-5, 3) on AB divides it in the ratio 3 : 2. Find :

(i) co-ordinates of point A

(ii) co-ordinates of point B

(iii) equation of line through point P and perpendicular to AB.

(iv) the point of intersection of the line (obtained in part (iii) above) and x-axis.

An empty tank can be filled by one pipe in 'x' minutes and emptied by another pipe in (x + 5) minutes. Both the pipes, when opened together, can fill the empty tank in 16.8 minutes. Find the value of x.

Use ruler and compass only to construct a triangle ABP such that AB = 8 cm, BP = 5 cm and angle ABP = 30°.

(i) Complete the rhombus ABCD such that P is equidistant from AB and BC.

(ii) Locate a point Q on line BP such that Q is equidistant from A and B.