Would like proof!(help please)

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.

Easy Math Editor

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Comments

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 - 7 years, 9 months ago

Thanks a lot!!!

Bhargav Das - 7 years, 9 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$