If two isosceles triangles have a common base, then prove that the line segment joining

If two isosceles triangles have a common base, then prove that the line segment joining their vertices bisects the common base at right angles.

Let ∆ABC and ∆DBC are the given triangles with same base BC, in which AB=AC and DB=DC.
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Also,Let AD meets BC at E.
To prove BE=CE and
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In ∆ABD and ∆ACD,
we have
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