Question

in triangle ABC 'H" is the orthocentre and "I" is the incentre. if angle BHC=angle BIC then the value of angle A is


please answer it fast please fast

Answer 1

Step-by-step explanation:

In general, in any triangle

"Angle BOC is equal to angle 2*A.

Angle BHC is equal to angle 180-A.

Angle BIC is equal to 90+A/2."

Let me know if you want the proof of above ones.

Now,H and I lie on the same circle implies that angle BHC is equal to angle BIC. (Angles in same segment theorem:The angle subtended by an arc or a line in a circle in the same segment are equal)

Hence,

90+A/2=180-A

implies A=60 degrees.

Hence, angle BOC is equal to 2*60=120 degrees.

You need not assume that it is an equilateral triangle as the other writer suggested.