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Vertices of a variable acute angled tria...

Vertices of a variable acute angled triangle `A B C` lies on a fixed circle. Also, `a ,b ,ca n dA ,B ,C` are lengths of sides and angles of triangle `A B C ,` respectively. If `x_1, x_2a n dx_3` are distances of orthocenter from `A ,Ba n dC ,` respectively, then the maximum value of `((dx_1)/(d a)+(dx_2)/(d b)+(dx_3)/(d c))+11` is a. `-sqrt(3)` b. `11-3sqrt(3)` c. `11+6sqrt(3)` d. `3sqrt(3)`

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