This is a Test of Mathematics Solution Subjective 110 (from ISI Entrance). The book, Test of Mathematics at 10+2 Level is Published by East West Press. This problem book is indispensable for the preparation of I.S.I. B.Stat and B.Math Entrance.

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*Let ABCD be a cyclic quadrilateral with lengths of sides AB = p , BC = q , CD = r, and DA = s . Show that *

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