Question

Let $a$, $b$ and $c$ be the three sides of a triangle. Show that $\frac{a}{b+c-a}+\frac{b}{c+a-b} + \frac{c}{a+b-c}\geqslant3$.

score 2.7k · Answer 1 · 2026-03-26 23:10:41

2.7k

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Let $a$, $b$ and $c$ be the three sides of a triangle. Show that $\frac{a}{b+c-a}+\frac{b}{c+a-b} + \frac{c}{a+b-c}\geqslant3$.

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List Question

Let $a$, $b$ and $c$ be the three sides of a triangle. Show that $\frac{a}{b+c-a}+\frac{b}{c+a-b} + \frac{c}{a+b-c}\geqslant3$.

Forbidden zones for circumcenter

How to prove that perpendicular bisector of line joining altitudes also bisects the side?

Triangle is separated into three triangles, how to calculate their areas?

Simplest proof that the edge of an inscribed equilateral triangle bisects the radius

Concentric Equilateral Triangles

Problem involving rhombus and its diagonals and height

Calculate the area of a triangular field, knowing that two and 1 angle.

The area of a triangle is $54\sqrt{6}$ square units. Find the lengths of the sides: $5x,6x,7x$

How to find a function that maps an element to row number in a triangle of integers?

Determine if a triangle is right angled with only coordinates

Name for line segment parallel to triangle base

Calculate 3rd point of a triangle, given 2 points and all angles in 2D

Trigonometry - how to find angles of triangle within another triangle?

Proof of a geometric statement

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