here is a picture for a problem my master asked me to solve it in the attachment

the question is prove that

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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

what is your opinion about this solution ???