Is this rule correct?

[Arsene Lupin]

Check out the following pic:



This is a circle with center C, and PQ is the diameter.

Can I take it as a rule that if the angle QPR = X, then QCR = 2X no matter where R is on the edge of the circle?

I saw an example where this was true, but couldn't find a source to support this rule. So I wanted to make sure.

Thanks for your help.

[Brent@GMATPrepNow]

Yep, that's true.

[dumb.doofus]

Well, keep one thing in mind though.. The theorem states:

The degree measure of an arc of a circle is twice the angle subtended by it at any point of the alternate segment of the circle with respect to the arc.

Just wanted to make sure that you understand that the theorem is true only for alternate segement.

[rah_pandey]

external angle of a triangle is sum of opposite internal angle. This is the basic rule and triangle in the figure is drawn inside a circle with given configuration is isosceles(two sides equal) thus the angle is always 2x