90-135 degree angle on vertice

Prove the largest angle in a triangle can not be one of over 135

degrees if the corners of the triangle must all touch the

circumference of the circle? The triangle is labelled ABC, and the

altitude from B is tanget to the circumcircle. I must then prove

that if the altitudes from B and C are tangent to the circumcircle,

what are the angles?

I realise that if it's greater than 135 degrees, and the intercepted arc is twice the the measure of the angle on the vertice. I do not know exactly how to go about proving it however, the >90 is obvious due to the cyclic quads etcetera but then i need to know how to place a limit on the angles. (135) And the 2nd part i dont know how to do at all.