If ABC be a triangle with pts. E and D on AB and AC respectively and AE.AB=AD.AC Then,prove that BEDC is a cyclic quadrilateral.

Note by Bhargav Das
4 years, 10 months ago

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Draw the circumcircle of the triangle $$BEC$$. Let $$X$$ be the second point of intersection of $$AC$$ with the circle.

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The Intersecting Chords Theorem tells you that $$AE\times AB = AX \times AC$$, and hence $$X$$ must be your point $$D$$. Thus $$BEDC$$ is cyclic.

- 4 years, 10 months ago

Thanks a lot!!!

- 4 years, 10 months ago