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in Sets, Relations and Functions by (67.7k points)
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In a triangle ABC , the line joining the circumcentre and incentre is parallel to BC, then Cos B + Cos C is equal to:

1 Answer

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Let `r` is the radius of the incircle and `R` is the radius of circumcentre.
As we are given line joining the circumcentre and incentre is parallel to BC in `Delta ABC`.
`:. r = RcosA=> r/R = cosA->(1)`
Also, we know the property,
`cosA+cosB+cosC = 1+r/R`
From (1),
`cosA+cosB+cosC = 1+ cosA`
`:. cosB+cosC = 1`

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