The question cannot possibly be right because the dimensions of an angle and arc-length are different.
Try using for the correct version of the question.
Hey all. At my school we have these things called "Real Problems" that we get every 3-4 weeks. This time it's about proofs. I have an A- in the class, so I got the difficult one with 4 very difficult (IMO) proofs.
I have NO idea where to start on this..I have drawn it out for you. All help is greatly appreciated. I am here to merely learn, not copy everything. I would appreciate full answers, but I am definitely here to Learn how to do this for tests.
Given: Tangent line AB and chord BC.
Prove: <ABC = (1/2)(arc)BC
In other words prove: (Angle ABC = Half of arc BC)
HINT: Using the center of the circle, draw in OB and OC (which I did in the picture for you).
1) How do we know this is not some sort of contest problem and our participation would be illegal?
2) How do we know this isn't an examination where outside help would be inappropriate?
3) If you really have NO IDEA, either you should not have been given the problem or the problem was intend to stretch you. In eaither case, outside influence will not accomplish the intent.
You start by gathering everything you know about chords and circles. There, now you know where to start.
So for the OBC triangle being isosceles the justification would be definition of an isosceles triangle?
Also,for 2<CBO + <COB = 180. and the other one, how do you know that? Is there a theorem or some justification for that? This would help me so I can fully understand and write the 2 column proof.
I'm to prove that angle ABC = half of arc BC though.
This is what my proof looks like right now:
1. Tangent line AB and chord BC 1. Given
2. Triangle CBO is isosceles 2. Angle sum theorem
3. 2<CBO + <COB = 180 3. ?
4. <CBO + <CBA = 90 4. ?
5. <COB = (arc)BC 5. ?
6. <ABC = (1/2)(arc)BC 6 ?