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.
Also visit: I.S.I. & C.M.I. Entrance Course of Cheenta
:
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
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.
Also visit: I.S.I. & C.M.I. Entrance Course of Cheenta
:
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