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4 votes
2 answers
320 views

Inequality from a point in plane to a triangle OR Inequality on a quadrilateral

If points $A$, $B$, $C$ form a triangle in euclidean space and $D$ is another point in the plane of the triangle, the problem is to show that : $\frac{AB}{DA + DB} + \frac{BC}{DB + DC} \ge \frac{AC}{...
Ritesh Ahuja's user avatar
3 votes
1 answer
160 views

Inequality in a triangle associated with Golden ratio

Let $ABC$ be arbitrary triangle, $D$, $E$, $F$ are the midpoints of $BC$, $CA$, $AB$ respectively. Define points, segments in the figure below. I am looking for a proof that: $$DE+EF+FD \le (DG+DH+EI+...
Đào Thanh Oai's user avatar