`Delta ` ABC is an isosceles triangle in which `AB = AC`. If `D` and `E` are midpoints of `AB` and `AC` respectively, prove that the points `B,C,E` and `D` are concyclic.

Explanation

In order to show that the points `B,C,E` and `D` are concyclic, we must prove that `/_ ECB + /_ EDB = 180^(@)`
Since `D` and `E` are the midpoints of `AB` and `AC` respectively, we have `DE || BC`.
Now,` DE ||BC`
`implies /_ ABC = /_ ADE`
`implies /_ ACE = /_ ADE ` ....(i) ` [ :' AB =AC implies /_ABC = /_ ACB ]`.
` :. /_ ECB + /_ EDB = /_ ACB+ /_ EDB`
`= /_ADE + /_ EDB ` [ using (i) ]
`= 180^(@)`
`[ :' /_ ADE` and `/_ EDB` form a linear pair ]
Hence, the points B,C,E and D are concyclic