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Trignometry

Cool goIITian

Joined:	18 Dec 2011
Post:	84

29 Jan 2012 19:04:45 IST

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Triangle

Mathematics

In a triangle ABC, the line joining the circumcentre to the incentre is parallel to BC, then CosB + CosC = ?

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hemang

Blazing goIITian

Joined: 27 Dec 2010

Posts: 1474

31 Jan 2012 10:43:36 IST

Like 4 people liked this

consider the triangle ABC.

let M be the incenter, and K be the circumcenter.

draw MD perepndicular to BC.

draw KE perpendicular o BC.

as angle BKC = 2*angle BAC,

so angle BKE = angle BAC.

also KM is parallel to BC.

KE = MD = r.

in triangle BEK,

cos(BKE) = cosA = r/R.

r = inradius = MD = KE, R = circumradius = KC = KR.

cosA + cosB + cosC = 1 + r/R

cosB + cosC = 1...

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