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Geometry Level 4

Let the equation x 3 + y 3 + 3 x y = 1 x^{3} + y^{3}+ 3xy = 1 represents the coordinate of one vertex A A and the equation of a side B C BC of the triangle A B C ABC . If B B is the orthocenter of the triangle A B C ABC , then the equation of side A B AB is y = m x + c y = mx + c . Then find the absolute value of 4 − m − c 4-m - c .


The answer is 3.

Archit Tripathi by Archit Tripathi , 23, India

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1 solution

Nikola Alfredi
Dec 23, 2019

It is a very tricky question. One must read it at least thrice... If you carefully look into the case when B is orthocentre then triangle ABC is Right angled at B, Thus making it easier to solve the problem. Now you just need to treat sides AB & BC as co-ordinate axes,... and done.

THIS IS JUST A HINT.... CAUSE THE QUESTION IS EASY. Try it out now...

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