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.

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## Problem:

:

If a, b and c are the lengths of the sides of a triangle *ABC* and if \( p_1 , p_2 \) and \( p_3 \) 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 )