Follow up on Triangles!

Geometry Level 4

Given a triange A B C ABC , construct squares A B P Q ABPQ and A C R S ACRS . Suppose that M M is midpoint of P R PR . Join M B MB and M C MC . Find M B M C \frac{MB}{MC} .

Details and Assumptions:

P P and C C are on opposite side of A B AB .

R R and B B are on opposite side of A C AC .


The answer is 1.

Kumar Saurav by Kumar Saurav , 24, India

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2 solutions

Ahmad Saad
May 2, 2016

2 Helpful 0 Interesting 0 Brilliant 0 Confused

I think there can not be a shorter and simpler solution than given by Ahmad Saad. But simple logic can be used to get the answer. For any triangle, it has to be the same ratio. I think it is termed an invariant. So that can only be 1 looking at the diagram.
It turns out that if squares are drawn on the sides of a quadrilateral similar result is obtained. There is a problem in Brilliant. Would it be true for any polygon ?

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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