In the given figure, O is the center of the circle, AB is diameter and CPD is a tangent to the circle at P. If ∠BPD = 30°, find :

(i) ∠APC

(ii) ∠BOP

(iii) ∠OAP

Given a line segment AB joining the points A(-4, 6) and B(8, 3). Find :

(i) the ratio in which line segment AB is divided by y-axis.

(ii) the co-ordinates of the point of intersection.

(iii) equation of perpendicular bisector of AB.

Use graph paper for this question. Take 1 cm = 1 unit on both the axes.

(i) Plot the points A(1, 1), B(5, 3) and C(2, 7).

(ii) Construct the locus of points equidistant from A and B.

(iii) Construct the locus of points equidistant from AB and AC.

(iv) Construct the point P such that PA = PB and P is equidistant from AB and AC.