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Let $\Delta ABC$ be an arbitrary triangle. On the three sides of $\Delta ABC$ , three regular $n$ -gons external to the triangle are drawn. Find all values of $n$ for which the centers of the $n$ -gons are vertices of an equilateral triangle.

#Geometry

Easy Math Editor

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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}`	$\boxed{123}$

Comments

i dont have any idea to solve it .please help me .@Calvin Lin @Sharky Kesa @Priyanshu Mishra Pkm

Abdullah Ahmed - 4 years, 9 months ago

Have you heard of the Mean Geometry Theorem?

Ameya Daigavane - 4 years, 8 months ago

Abdullah Ahmed - 4 years, 8 months ago

please give me a full proof solution . I can't do it .

Abdullah Ahmed - 4 years, 4 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}`	$\boxed{123}$

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Comments

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