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# Test of Mathematics Solution Subjective 107 - Perpendiculars from Center  This is a Test of Mathematics Solution Subjective 107 (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

## Problem:

If a, b and c are the lengths of the sides of a triangle ABC and  if and are the lengths of the perpendiculars drawn from the circumcentre onto the sides BC, CA and AB respectively, then show that .

## Solution

:
Let  O be the circum centre = 2 Similarly, & Now, = = = Lemma
For &             (lemma proved)

So, = [ as ]
= =  ( proved ) This is a Test of Mathematics Solution Subjective 107 (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

## Problem:

If a, b and c are the lengths of the sides of a triangle ABC and  if and are the lengths of the perpendiculars drawn from the circumcentre onto the sides BC, CA and AB respectively, then show that .

## Solution

:
Let  O be the circum centre = 2 Similarly, & Now, = = = Lemma
For &             (lemma proved)

So, = [ as ]
= =  ( proved )

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