>How would I construct

>(A) an isosceles triangle if only given the altitude to the

>base and a base angle? This is the same as constracting a right triangle, given a side and an angle.

>

>(B) an isosceles trapezoid if only given the bases and the

>diagonal?

Drop perpendiculars from the endpoints of the smaller base.

>

>(C) a right triangle given the leg and the radius of the

>circumscribed circle?

An inscribed angle that subtends a diameter of a circle is right.