Inequality for two triangles with the same base

Question

Take 2 triangles, $ABC$ and $OBC$, with the same base $BC$.

If $\angle A<\angle O$, then $AB+AC>OB+OC$.

This question is derived from the textbook question - for a point $O$ in the triangle $ABC$, $AB + AC > OB + OC$.

The textbook question has been solved, and the one I asked is just a more general case. Intuitively it holds, but can anyone prove it arithmetically?

It doesn't look true. When angle(A) is given, $A$ belongs to a arc of circle which chord is segment $BC$ https://en.wikipedia.org/wiki/Inscribed_angle#Theorem Thus for a given angle the sum $AB + AC$ belongs to a certain interval of values. By modifying slightly the angle, the interval is slightly modified and one can find inequalities in both senses for $OB + OC$ and $AB + AC$ — Gribouillis, Jan 24 '22 at 14:52

score 0 · Accepted Answer · answered Jan 24 '22 at 15:04

0

It's not true as the picture show

answered Jan 24 '22 at 15:04

Essaidi

Yes.... Thank you, I had taken very generic cases, thus I was led to the belief. – Abhiraj Roy Jan 24 '22 at 15:46

1 Answers1