http://img69.imageshack.us/img69/5044/imagemta.jpg

Hypothesis: AC = CB

DE is the diameter

CH is perpendicular to AB (the altitude)

Thesis: DE : BC = BC : CH (BC^2 = DE * CH)

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- Sep 6th 2011, 12:21 AMgobyProof: An Isosceles Triangle inscribed in a Circle
http://img69.imageshack.us/img69/5044/imagemta.jpg

Hypothesis: AC = CB

DE is the diameter

CH is perpendicular to AB (the altitude)

Thesis: DE : BC = BC : CH (BC^2 = DE * CH) - Sep 6th 2011, 12:46 AMalexmahoneRe: Proof: An Isosceles Triangle inscribed in a Circle
$\displaystyle A=\frac{1}{2} *AB*CH$

$\displaystyle R=\frac{AB*BC*CA}{4A}$ (Circumradius - AoPSWiki)

$\displaystyle R=\frac{AB*BC*CA}{4*\frac{1}{2}*AB*CH}$

$\displaystyle R=\frac{BC*CA}{2CH}$

$\displaystyle R=\frac{BC^2}{2CH}$

$\displaystyle \frac{BC^2}{CH}=2R=DE$

$\displaystyle BC^2=DE*CH$ - Sep 6th 2011, 01:19 AMgobyRe: Proof: An Isosceles Triangle inscribed in a Circle
Okay, I understood it, but what's the proof for R = http://mathworld.wolfram.com/images/...s/Inline22.gif?

- Sep 6th 2011, 01:25 AMalexmahoneRe: Proof: An Isosceles Triangle inscribed in a Circle