求教 TT GWD-12-8

lguo1

    

Q8:  (I'm sorry that the figure cannot be pasted and Pi becomes p in the choices)

    

In the figure shown, the triangle is inscribed in the
semicircle.  If the length of line
segment AB is 8 and the length of line segment BC is 6, what is the length of
arc ABC?

    

 
A.          15p

    

B.          12p

    

C.          10p

    

D.          7p

    

E.          5p

The given right answer is E.   I know it is correct.  I have one question though: according to the conditions given
in the original question, will <ABC be equal to 90 for sure or it may be equal to some other value as well?
How could we prove it using math formulas?

Thanks!

wangwei1016_

<ABC be equal to 90 for sure ,可以证明.

直径所对的圆周角是直角。

lguo1

You are right wangwei.  I remember it now. 
Thank you very much!