is a chord of a circle with centre  O  :  A is a point on an minor arc  BC. Then  ∠BAC − ∠OBC is equal to

The problem seems to be incomplete. However, based on the given information, we can use the properties of circles to solve the problem.

Step 1: Identify the given information. We know that BC is a chord of the circle with center O, and A is a point on the minor arc BC.

Step 2: Use the property of circles that states that the angle subtended by a chord at the center is twice the angle subtended by it at any point on the alternate segment. This means that ∠BOC = 2∠BAC.

Step 3: Subtract ∠OBC from both sides of the equation to isolate ∠BAC. This gives us ∠BAC - ∠OBC = 1/2 ∠BOC - ∠OBC.

Without additional information, we cannot determine the exact values of the angles. However, the relationship between ∠BAC, ∠OBC, and ∠BOC is given by the equation ∠BAC - ∠OBC = 1/2 ∠BOC - ∠OBC.