Let ABCD be a cyclic quadrilateral with lengths of sides AB = p , BC = q , CD = r, and DA = s . Show that
Discussion:
Since ABCD is cyclic is similar to
(since
as they are subtended by the same arc AD, and
as vertically opposite angles are equal)
Hence their corresponding sides are proportional.
Similarly is similar to
Hence
Hence
Finally we note that since is similar to
.
This proves that