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If the incircle of the triangle ABC passes through its circumcentre, then prove that cosA +cosB+cosC = √2



If the incircle  of the  triangle ABC passes through its circumcentre, then prove that cosA


+cosB+cosC = √2


 

Grade:12

1 Answers

SAGAR SINGH - IIT DELHI
878 Points
13 years ago

Dear student,

The circle passing through the vertices of the triangle ABC is called the circum-circle. Its radius R is called the circum-radius. In the triangle

ABC, R = a/2 sin A = b/2 sin B = c/ 2 sin C = abc/4Δ.

1874_Circum-circle.JPG

From here we can deduce that 

cosA+cosB+cosC = √2

 

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Sagar Singh

B.Tech, IIT Delhi

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