BC is a chord with centre O. A is a point on an arc BC . Prove that: `angleBAC+angleOBC= 90` , if A  is the point on the major arc.

Explanation

The arc BC for the `angleBOC = z` on the center of circle and `angleBAC = x` and `z = 2x`

Now apply the property of angle sum property of triangle

In `triangleBOC`

`angleOBC+angleOCB+angleBOC=180^*`

`y+y+z=180^*`

`2y+2x=180^*`

`x+y=90^*`

Hence, `angleBAC+angleOBC=90^*`