Question

The measure of an inscribed circle of an angle is the measure of the intercepted arc

Answer 1

(the statement does not appear to be true)

Explanation:

I don't think the statement is true, but you CAN compute the intercepted arc from the angle.

Note that BFDG is a convex quadrilateral, so its angles sum to 360. Since we know the inscribed circle touches the angle tangentially, angles BFD and BGD are both right angles, with a measure of 90 degrees.

Therefore, adding the angles together, we have:

alpha + 90 + 90 + <FDG = 360

Therefore, <FDG, the inscribed angle, is 180-alpha (ie, supplementary to alpha)