Question: Where do you think you're going?

How to find the minimum of (3*a/sqrt(1-u^2)+b/sqrt(1-t^2))/c under the constraints
{a^2+2*b*c*u >= b^2+c^2, a*t+b*u <= c, b^2*(t^2-u^2)/(t^2-1)+c^2 <= 2*b*c*u}, assuming all variables nonnegative, with Maple? Both  DirectSearch:-GlobalOptima and Optimization:-Minimize  fail in it
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