Set of problems from Thailand 1st round math POSN (help mehhh)

It's almost a year passed, but I still can't do these problems. Most of them I already did it, but I will still post it anyway. There're 4 main topics and Inequalities for the glory of satan of course.

I'll be translating these problems in English for you. Might take about 10 minutes each topics.

Please help mehhh!

Thanks!

P.S: Every single note I wrote it as 2014, which is supposed to be 2013. I can't change it lol. =="

Please post a full solution to these notes instead, not on this note. Someone even did the problem before I finished translating. It was expected to be 3-hour test! =..="

Geometry (I did 1 and 3, the rest are stuck midway)

Algebra (I did 1 (bashing) and 2.1)

Inequalities (I did only 1)

Number Theory (can't remember anything I did)

Combinatorics (I did all of them except 3, and 5 seems to be wrong)

#OlympiadMath #HelpMe!

Easy Math Editor

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Comments

For the first one, I have transformed the
Quadrilateral into a rectangle of the same area. But am having difficulty in transforming the rectangle into a square.

A Former Brilliant Member - 6 years, 8 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}`	$\boxed{123}$