Use ruler and compass for the following construction:

(a) construct an equilateral triangle ABC of side 5 cm.

(b) construct the circumcircle of ΔABC.

(c) construct the locus of points which are equidistant from AB and BC. Mark the point where the circumcircle and locus meet, as D.

(d) give the geometrical name of quadrilateral ABCD.

The cost price of a TV set is ₹ 20,000. The shopkeeper marked it for ₹ 24,000. He sells it to a customer at a discount of 10% on the marked price. If the sale is intra-state and the rate of GST is 12%, find the:

(a) discounted price of the TV set.

(b) amount paid by the customer to clear the bill.

In the given diagram, DE || BC and AD : DB = 2 : 3.

(a) Prove that : ΔADE ~ ΔABC and hence find DE : BC.

(b) Prove : ΔDFE ~ ΔCFB

(c) Given, area of ΔDFE = 16 square units, find the area of ΔCFB.