Hi, can any triangle be divided into isosceles triangles? How to prove or disprove that? Thanks a lot.

Hello,
What do you think about considering the circumscribed circle ?

Let ABC be the triangle and O be the center of this circle.
OA=OB=OC.

So it may be interesting to see the properties of triangles OAB, OAC and OBC

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Everything is possible. The impossible just takes longer.

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Ah, right, silly me.

Moo, I see that you've posted A LOT since my last visit here.

Thanks.

In my opinion this is only possible if the triangle doesn't contain an obtuse interior angle.

Then the center of the circumscribed circle is outside the triangle and at least 2 of the radii are placed outside the triangle too.

I see your point here. But still, maybe there's a different way of proving that property for an obtuse-angled triangle?

LoL, I think I got it.

You can always inscribe a circle in a triangle. Then, connecting the points of tangency with the sides of the triangle to the center of the circle and drawing another triangle whose vertices are also those tangency points, we obtain six isosceles triangles within the original one.

Don't you guys think so?

Good spot !

__________________
Everything is possible. The impossible just takes longer.

- I hate, I can't stand, I abhor, I dislike, I disdain, I detest, I loathe, I despise and I am repelled by tousled birds of pray.