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Equilateral Triange inside a circle

Hello all,

I'm hoping someone can help with this one, I'm not sure why I'm not seeing it (Worried). I've attached a picture from my text book and an answer I've found but don't quite understand.

Question:

An equilateral triangle where each side's length equals x is inscribed in a circle of radius r. Show that:

$\displaystyle

r^2=\frac{x^2}{3}

$

An answer I've found already but don't understand:

http://www.mathhelpforum.com/math-he...47e38684-1.gif

http://www.mathhelpforum.com/math-he...beedce3c-1.gif. Thus:

http://www.mathhelpforum.com/math-he...d663fb68-1.gif. Solve for rē and you'll get:

http://www.mathhelpforum.com/math-he...fe70daf7-1.gif

However, I'm not sure how one is supposed to know that $\displaystyle r=\frac{2}{3}\cdot h$ everything else made sense though...

Thanks,

Skilo

Equilateral triangle inside a circle

Posted by Skilo

Using Soroban's nice diagram apply the 30-60-90 triangle rule.

If hypothenuse is 2 the side opposite the 30 angle =1. the side opposite the 60 angle = radical 3 What is angle ACG .Can you prove it.

bjh