# 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.

Consider the kite ABCD.

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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in 1 and 2 locus is perpendicular biseators of AC and BD respectivily

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