Given information:
- In the given figure, AOB is a diameter of a circle with center O.
- AC is a tangent to the circle at A.
- Angle BOC is given as 130°.

Proof:
To prove that angle BOC is 130°, we will use the properties of angles in a circle.

1. Angle in a semicircle:
- A diameter of a circle divides the circle into two equal parts, known as semicircles.
- The angle formed at any point on the circumference of a circle, when the lines joining the point to the endpoints of a diameter, is always 90°.
- Therefore, angle BOC is a right angle, and its measure is 90°.

2. Tangent and radius:
- A tangent to a circle is perpendicular to the radius drawn from the center of the circle to the point of contact.
- In the given figure, AC is a tangent to the circle at A.
- Therefore, angle OAC is 90°.

3. Angle sum property:
- In a triangle, the sum of all angles is always 180°.
- In triangle OAC, angle OAC + angle OCA + angle OAC = 180°.
- Since angle OAC and angle OCA are both 90° (as proved in the previous steps), we can substitute their values into the equation.
- 90° + 90° + angle OAC = 180°.
- Simplifying the equation, we get angle OAC = 0°.

4. Exterior angle property:
- The measure of an exterior angle of a triangle is equal to the sum of the measures of its interior opposite angles.
- In triangle OAC, angle OAC is the exterior angle.
- The interior opposite angles are angle OCA and angle OAC (both 90°).
- Therefore, angle OAC = angle OCA + angle OAC.
- Simplifying the equation, we get angle OCA = 0°.

5. Angle BOC:
- Angle BOC is formed by the lines OB and OC, which are radii of the circle.
- The measure of angle BOC is equal to the sum of the measures of angles OCA and OCB.
- From the previous steps, we know that angle OCA = 0°.
- Therefore, angle BOC = angle OCB + angle OCA = angle OCB + 0°.
- Simplifying the equation, we get angle BOC = angle OCB.

Conclusion:
- Angle BOC is a right angle (90°) and angle OCB is equal to angle BOC.
- Therefore, angle BOC = angle OCB = 90°.
- The given angle BOC is 130°, which contradicts our conclusion.
- Hence, there is an error in the given information or figure.