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avatar+363 

A circle centered at O is circumscribed about Triangle ABC as follows:

https://latex.artofproblemsolving.com/e/3/3/e3327b08d906e6cc74d5f9f0232a3016dea5197b.png

What is the measure of BAC?

 

I think this question was answered before but the person who answered it didn't explain how they got their answer. 

 May 6, 2021
 #1
avatar+121055 
+3

Since O  is  the  center......the measure of angle  COA  = (360  - 100 - 110) =  150

 

And  triangle COA  is  isosceles with OC = OA

 

So  angle OAC  =  (180 - 150) /2  =  15

 

And triangle  BOA is also  isosceles with OB = OA

 

So  angle OAB  = ( 180 - 110)  / 2   =   35

 

So angle BAC  = angle OAB + OAC  =  35  + 15   =  50°

 

 

Another (easier)  way to see this is to note  that central angle BOC  =100

 

And angle  BAC  is  an inscribed angle which subtends the same arc as BOC

 

So...its measure  = (1/2)  of BOC  = (100) / 2  =   50°

 

 

cool cool cool

 May 6, 2021
 #2
avatar+363 
+2

Thank you

 May 6, 2021
 #3
avatar+121055 
+1

No prob  !!!

 

 

cool cool cool

CPhill  May 6, 2021

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