Just for the isosceles?

Geometry Level 2

It is easy to see that if two sides of a triangle are equal (i.e. if the triangle is isosceles), then the corresponding angle bisectors are equal as well.

What about the converse?

In a given triangle ABCABC , BDBD and CECE are the angle bisectors of B\angle B and C\angle C respectively.

If BD=CE\left| {\overline {BD} } \right| = \left| {\overline {CE} } \right|, is it necessarily true that AB=AC\left| {\overline {AB} } \right| = \left| {\overline {AC} } \right|?

Hint: Angle bisector theorem might be useful.


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