(a) Construct the locus of a moving point which moves such that it keeps a fixed distance of 4.5 cm from a fixed-point O.

(b) Draw line segment AB of 6 cm where A and B are two points on the locus (a).

(c) Construct the locus of all points equidistant from A and B. Name the points of intersection of the loci (a) and (c) as P and Q respectively.

(d) Join PA. Find the locus of all points equidistant from AP and AB.

(e) Mark the point of intersection of the locus (a) and (d) as R. Measure and write down the length of AR.

(Use a ruler and a compass for this question.)

Construct a regular hexagon ABCDEF of side 4.3 cm and construct its circumscribed circle. Also, construct tangents to the circumscribed circle at points B and C which meets each other at point P. Measure and record ∠BPC.

(Use a ruler and a compass for this question.)

A tree (TS) of height 30 m stands in front of a tall building (AB). Two friends Rohit and Neha are standing at R and N respectively, along the same straight line joining the tree and the building (as shown in the diagram). Rohit, standing at a distance of 150 m from the foot of the building, observes the angle of elevation of the top of the building as 30°. Neha from her position observes that the top of the building and the tree has the same elevation of 60°.

Find the:

(a) height of the building

(b) distance between

1. Neha and the foot of the building
2. Rohit and Neha
3. Neha and the tree
4. building and the tree.

A life insurance agent found the following data of age distribution of 100 policy holders, where f is an unknown frequency.

(a) If the mean age of the policy holders is 35.65 years, find the unknown frequency f.

(b) Find the median class of the distribution.