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Geometry Level 3

In a triangle A B C ABC

1 a + c + 1 b + c = 3 a + b + c \frac{1}{a+c}+ \frac{1}{b+c}= \frac{3}{a+b+c}

∠ C \angle C in degrees is


The answer is 60.

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Rakshit Joshi by Rakshit Joshi , 26, India

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2 solutions

Ayush G Rai
Nov 7, 2016

Relevant wiki: Cosine Rule (Law of Cosines)

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a real fast trick is to put a=2Rsin(A) i.e sine rule to convert everything into angles, followed by using formulae for sum in LHS and accordingly solving.

Ajinkya Shivashankar - 4 years, 7 months ago

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good one..

Ayush G Rai - 4 years, 7 months ago

thanks for your suggestion, nice and comfortable.

Rakshit Joshi - 4 years, 7 months ago

oh wow! nice use of cosine formula. well if you won't had to take k = a + b + c k= a+b+c , just add in the l . h . s l.h.s and then cross multiply, after then use cosine rule problem is done, it just saves time and nothing else. Anyways good solution :)

Rakshit Joshi - 4 years, 7 months ago

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Well the truth is that I don't like to deal with too many variables.#2is better than3

Ayush G Rai - 4 years, 7 months ago

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haha good reply

A Former Brilliant Member - 4 years, 7 months ago

oh, ok . same here ;)

Rakshit Joshi - 4 years, 7 months ago

I did it entirely based on instinct!

William Nathanael Supriadi - 4 years, 7 months ago
Joe Potillor
Nov 8, 2016

That's a 6 instead of a 3, hopefully you'll like the solution.

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