# what is your opinion in that problem

• Aug 11th 2011, 04:33 PM
mido22
what is your opinion in that problem
here is a picture for a problem my master asked me to solve it in the attachment
the question is prove that $\displaystyle c/Sin C = 2r$
here is my proof :
Construction : draw MD perpendicular to AB chord
Proof :
since -->MD perpendicular to AB
so -->MD bisects <M
so -->Sin <BMD = opposite / hypotenuse = BD / r
since --><M and <C two angles subtended by same arc
so --><C = 0.5 * <M = <BMD
so -->sin C = BD / r
since -->BD = 0.5 * side c
so -->sin C = (0.5*c)/r
so -->r = (0.5*c)/sin C (multiplication the equation by 2)
so -->2r = c / sin C and that is required to prove

• Aug 11th 2011, 05:10 PM
skeeter
Re: what is your opinion in that problem
Quote:

Originally Posted by mido22
here is a picture for a problem my master asked me to solve it in the attachment
the question is prove that $\displaystyle c/Sin C =$$\displaystyle r^2$ ***
here is my proof :
Construction : draw MD perpendicular to AB chord
Proof :
since -->MD perpendicular to AB
so -->MD bisects <M
so -->Sin <BMD = opposite / hypotenuse = BD / r
since --><M and <C two angles subtended by same arc
so --><C = 0.5 * <M = <BMD
so -->sin C = BD / r
since -->BD = 0.5 * side c
so -->sin C = (0.5*c)/r
so -->r = (0.5*c)/sin C (multiplication the equation by 2)
so -->2r = c / sin C and that is required to prove

I agree with your proof that $\displaystyle \frac{c}{\sin{C}} = 2r$ ... but what about $\displaystyle \frac{c}{\sin{C}} = r^2$ *** ? is that a typo?