If the line joining circumcentr and incentre is parallel to BC then cosB+cosC=

SO ANSWER IS I.E COSB+COSC=1 HERE this angle theta is the angle between IO and LO it is zero in this case so our answer is one.

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Drop perpendiculars from I and O on to BC and let the feet of the perpendiculars be P and Q resp.

 

IP = in-radius = r.

 

Also OQ = R cos A.

 

Since OI is parallel to BC, we have IP = OQ i.e. r = R cos A and hence

 

 

 

We know that 

 

Thus we obtain