Question

BC is a chord of a circle with centre O. A is a point on major arc BC as shown in the figure.

Prove that

BAC OBC 90  +  = .​

Answer 1

Angle BOC = 2*angle BAC =2y ( central angle is twice the inscribed angle subtended by a chord in a circle)

AngleOBC = angle OCB = x ( as OB = OC, being radii of the same circle)

To prove out: x+ y =90

Now in triangle OBC,

2x + 2y =180° ( angle sum property if a triangle)

=> 2(x+y) = 180°

=> x+y = 90°