construct a kite ABCD,such that BD=10cm,AD=7cm,AB=5cm.

- Construct the locus of a point equidistant from vertices A and C.
- Construct the locus of a point equidistant from B and D.
- name the loci in 1. and 2.

Steps of construction:

1) Draw diagonal BD = 10 cm

2) Now, with B as centre and some radius, cut an arc on both the sides of line BD. Similarly, with D as centre and some radius, cut two arcs intersecting the two previous arcs at P and Q. Join PQ , thus constructing the perpendicular bisector of BD.

3) With B as centre and radius 5 cm, cut an arc on the perpendicular bisector. Mark this point as A. Join AB

4) With A as centre and radius 7 cm, cut an arc on the perpendicular bisector. Mark this point as D. Join AD.

4) With D as centre and radius 7 cm, cut an arc on the perpendicular bisector. Mark this point as C. Join DC.

5) Join BC.

Thus kite ABCD is constructed.

The perpendicular bisector of B and D form the locus of a point which is equidistant from vertices B and D.

Also, we need to construct the locus of a point equidistant from vertices A and C.

So, the perpendicular bisector of A and C form the locus of a point which is equidistant from vertices A and C.

For this, with A as centre and some radius, cut an arc on both the sides of line AC. Similarly, with C as centre and some radius, cut two arcs intersecting the two previous arcs at P and Q. Join PQ , thus constructing the perpendicular bisector of AC.

Therefore, the perpendicular bisector of AC form the locus of a point which is equidistant from vertices A and C.

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