Triangle inscribed within a circle

[BrownianMan]

ABC inscribed within a circle whose diameter AC forms one of the sides of hte triangle. If Arc BC on the circle subtends an angle of 40 ddegrees, find the measure of angle BCA within the triangle

 

[Quinzio]

What's your idea ?
Any drawing ?

 

[BrownianMan]

I haven't done this kind of thing since high school. Could you explain how you measure inscribed angles? My initial guess is that one of the sides is 90, one 40, and the other must be 50...

 

[Mentallic]

Yes that's right. Because whenever you have a triangle with one of its sides being the diameter of the circle, then the opposite angle to that side will be 90^o.

 

[HallsofIvy]

If angle A has its vertex on a circle and subtends an arc of $\theta$ degrees, then the measure of the angle is $\theta/2$ degrees. You are given that one angle of the triangle subtends an arc of 40 degrees and another an arc of 90 degrees.