Question

In triangle ABC , the bisectors of angle B and angle C meet at O . prove that angle BOC =90 + 1/2 angle A ​

Answer 1

Step-by-step explanation:

In the triangle of ABC-

AngleA+angleB+angleC=180°

or,1/2ofA+1/2ofB+1/2ofC=90°

or,1/2ofB+1/2ofC=90°-1/2ofA (eqution number 1)

In the triangle of OBC-

AngleOBC=1/2ofB [2]

and OCB=1/2ofC[3]

in the teiangle of OBC-

angleBOC+angleOCB+angleOBC=180°

angleBOC+1/2ofC+1/2ofB=180° [from 2 and 3]

angleBOC+90-1/2ofA=180°[from equation 1]

angleBOC=180°-90°-1/2ofA

angleBOC=90°-1/2ofA