A Geometry Question...

Let $ABCD$ be a convex quadrilateral such that $\angle DAB$ is acute. $\angle ADB$ and $\angle ACB$ are complementary angles. $\angle DCB$ and $2 \angle DBA$ are supplementary angles. Show that $(DB+BC)^2 = AD^2+AC^2$ .

I don't get how I can relate the angles and the sides. Perhaps, by proving one of them a right $\triangle$ .

#Geometry

Easy Math Editor

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Comments

I haven't solved it, but i think you should try dropping perpendiculars, extending line segments and using similar triangles, and if a right triangle pops up, using Pythagoras.

Sachetan Debray - 5 months, 3 weeks 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}`	$\boxed{123}$