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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, 6 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.

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Thanks a lot!!!

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TopNewestDraw the circumcircle of the triangle \(BEC\). Let \(X\) be the second point of intersection of \(AC\) with the circle.

alt text

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.

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Thanks a lot!!!

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