ScholMaths
New member
- Joined
- Apr 30, 2012
- Messages
- 9
The following is a question from a very old high school exam paper I am trying to solve (for the challenge):
Given that 4sin(A/2)sin(B/2)sin(C/2)=cosA+cosB+cosC-1 show that the line joining the incentre to the circumcentre of a triangle ABC is inclined to BC at an angle:
tan-1((cosB+cosC-1)/(sinB-sinC))
I have drawn a clear diagram. I can see that if the tangent of the required angle =x/y then x can be taken as the radius, r say, of the incircle but I am stuck on getting the corresponding y.
Any help would be much appreciated.
Given that 4sin(A/2)sin(B/2)sin(C/2)=cosA+cosB+cosC-1 show that the line joining the incentre to the circumcentre of a triangle ABC is inclined to BC at an angle:
tan-1((cosB+cosC-1)/(sinB-sinC))
I have drawn a clear diagram. I can see that if the tangent of the required angle =x/y then x can be taken as the radius, r say, of the incircle but I am stuck on getting the corresponding y.
Any help would be much appreciated.