let n-1, n, n+1 be 3 consecutive integers
So
(n+1)^2= n^2+ (n-1)^2
(n+1)^2-(n-1)^2= n^2
4n = n^2
So n = 0 or n = 4
n can?t be 0 as n-1 will be negative then
So 3,4 and 5 is the only triplet formed.
Since it is an isosceles trapezium
So angle C = angle D = x
let A = 180 ?D = 180 ?x (since AB is parallel to CD)
B = 180-x
A+C = 180 ?x + x = 180 degrees (Property of cyclic quadrilateral)
ABCD is cyclic parallelogram with AB // CD and AD // BC
Considering angles A = C = y (Property of parallelogram) and B=D = x Also since it is cyclic A+C = B+D = 180 degrees
So x=y=90 degrees And also opposite sides are equal being a parallelogram
Thus ABCD is a rectangle
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