A circle is circumscribed around triangle ABC, find length?

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To find the lengths of arcs AB, BC, and CA in a triangle circumscribed by a circle, the angles subtended at the center must be determined first. The arc length formula, l = rθ, applies, where θ is the angle in radians. The discussion emphasizes that the angles of the triangle relate to the angles subtended at the circle's center, with each arc length being proportional to its respective angle. Participants also clarify that the notation used in the problem refers to subquestions, and confusion arises regarding the relationship between triangle angles and the circle's radius. Understanding these relationships is crucial for correctly calculating the arc lengths.
  • #31
Buffu said:
Yes sorry it is angle c.

Your figure should be like this :-
View attachment 205456
sorry, but I still have questions regarding that..
the tetha times R is to find Arc AC right?
while tetha is twice angle ABC ?
 
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  • #32
Helly123 said:
sorry, but I still have questions regarding that..
the tetha times R is to find Arc AC right?
while tetha is twice angle ABC ?

For ##2\pi - \theta## not ##\theta## I drew theta other way because it was difficult to draw on the correct side.
 
  • #33
Buffu said:
Yes sorry it is angle c.

Your figure should be like this :-
View attachment 205456
Can i say 2phi - theta = twice angle ABC?
 
  • #34
Helly123 said:
Can i say 2phi - theta = twice angle ABC?

Yes.
 
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  • #35
Try to use the previous arc length equation and the law of cosines to find different arc length segments of the circle and work from there
 
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