Question

The circumcenter of triangle abc is o.prove that angle obc+angle bac=90

Answer 1

here is your answer.....

Answer 2

Let
Angle OBC = x°
Angle BAC = y°

Now,
We know that we can draw a circle around triangle as it's centre be circumcentre which touchcs corners of triangle:-
Draw a picture as shown in attachment,

In triangle OBC
OB = OC
So,
Angle OBC = Angle OCB = x°

Now,
Consider Arc BC,
We know that. An arc subtended twice of angle at circum when compared to centre,
Therefore,
Angle BAC = 2× angle BOC = 2y

Now,
in Triangle OBC
Sum of Angels = 180°

2y + x + x = 180°

x + y = 90°

or,
Angle OBC + Angle BAC = 90°