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densk [106]
3 years ago
8

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

Mathematics
1 answer:
Andre45 [30]3 years ago
4 0

Answer:

(the statement does not appear to be true)

Step-by-step 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)

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