Question

If in a triangle abc, the line joining the circumcentre and incentre is parallel to bc,then cos b +cos c

Answer 1

Answer:

In △OBL,cosA=

OB

OL

=

R

r

⇒RcosA=r

⇒RcosA=4Rsin

2

A

sin

2

B

sin

2

C

⇒cosA=4sin

2

A

sin

2

B

sin

2

C

⇒cosA=cosA+cosB+cosC−1

⇒0=cosB+cosC−1⇒cosB+cosC=1

Step-by-step explanation:

hope it was useful.

Answer 2

Answer:

In △OBL,cosA=

OB

OL

=

R

r

⇒RcosA=r

⇒RcosA=4Rsin

2

A

sin

2

B

sin

2

C

⇒cosA=4sin

2

A

sin

2

B

sin

2

C

⇒cosA=cosA+cosB+cosC−1

⇒0=cosB+cosC−1⇒cosB+cosC=1