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 ???