Proving angle equivalency

Dec 2015
3
0
New Hampshire
IMAG0034.jpg

Hi everyone,

Is there a way to prove that angle B and angle C are equivalent in this situation? The argument my textbook made certainly seemed to imply that, and it really bothers me that I can't quite see it. I'm worried it's really simple and I'm overthinking it... I haven't taken geometry in nearly ten years but I tried to review the basics.

To be clear, the arc is all part of one circle (if that matters) and there are no parallel or perpendicular lines (aside from the perpendicular radius to tangent).

Any help is greatly appreciated!
 

HallsofIvy

MHF Helper
Apr 2005
20,249
7,909
Are we to assume that the unlabeled point at the bottom is the center of the circle? If so, then use the fact that the base angles of an isosceles triangle are congruent.
 
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Dec 2012
1,145
502
Athens, OH, USA
You just need the inscribed angle theorem:

 
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Dec 2015
3
0
New Hampshire
Thank you both so much, I've got it now! (and yes HallsofIvy, that point at the bottom is the center of the circle; I should have labeled it as such).

I'll definitely have to keep that inscribed angle theorem in mind for the future.