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.
–
Mark Hennings
·
3 years, 6 months ago

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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. – Mark Hennings · 3 years, 6 months ago

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– Bhargav Das · 3 years, 6 months ago

Thanks a lot!!!Log in to reply