Inscribed circle in triangle

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krypic

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Hello, I was hoping you guys would be able to help me with this problem. There is an inscribed circle O in triangle ABC. I need to prove that angle BOC is supplementary to angle AOB. Im pretty stumped as to how to solve this. I realize that BOAC is a kite and so its diagonals will be perpendicular but im not sure this is the right direction. Any help would be greatly appreciated.InscribedCircle.gif
 
krypic said:
Hello, I was hoping you guys would be able to help me with this problem. There is an inscribed circle O in triangle ABC. I need to prove that angle BOC is supplementary to angle AOB. Im pretty stumped as to how to solve this. I realize that BOAC is a kite and so its diagonals will be perpendicular but im not sure this is the right direction. Any help would be greatly appreciated.View attachment 8234
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View attachment 8234

There is something wrong!! If "angle BOC is supplementary to angle AOB" then BOC + AOB = 180° → AOC = 180° → r = 0 → the whole thing becomes dimensionless!!

Am I reading it correctly?
 
Here it is straight from the book. #43
 

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Ok i think i solved it. It doesnt state its a kite, i just thought u could derive to it. however, i tried the approach ofproving that triangle BOC is congruent to triangle AOC. Also, I stated that the circle is divided into 3 equal parts by the perpendicular segments OA, OB, OC. 360 / 3 = 120. Angle BOC = AOC by CPCTC. So, angle BOC = 60. I did this to every side. Then I said AOB = AOC + BOC. 60 + 60 = 120. So AOB + BOC = 180. supplementary.
 
Sorry, I realize now that I forgot to use lower case letters. This must have been very confusing for all of you :???:
 
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