3) Find the value of x.

In the given image, we have a circle with center O and points B and C on the circumference. The line segment OB is a radius, and the line BC is tangent to the circle at point B. The angle BOC is given as 54 degrees, and we need to find the angle OBC, which is labeled as x.

Since the line BC is tangent to the circle at point B, the radius OB is perpendicular to the tangent line BC at the point of tangency. Therefore, the angle OBC is 90 degrees.

However, the image shows that OB is a radius, OC is a line segment, and BC is a tangent. The angle labeled 54 degrees is between OB and OC. The angle labeled x is between OC and BC. The point O is the center of the circle.

Let's re-examine the image. It appears that OC is a line segment, and OB is a radius. The angle between OC and the tangent BC is labeled as x. The angle between the radius OB and the line segment OC is labeled as 54 degrees. There is a point C outside the circle, and a line segment from C touches the circle at B.

If OC is a secant line, and BC is a tangent, then we would have different relationships.

Let's assume the diagram implies that OB is a radius and BC is a tangent at B. The angle between OC and OB is 54 degrees. The angle between OC and BC is x. We are looking for x.

In triangle OBC, OB is the radius. BC is the tangent at B. Thus, the angle between the radius OB and the tangent BC is 90 degrees (OB ⊥ BC). This means ∠OBC = 90°.

The angle ∠BOC is not directly given, but the angle between OB and OC is 54°. The angle x is ∠OCB.

In △ OBC, we have:

• OB = radius
• BC = tangent
• ∠OBC = 90° (radius is perpendicular to tangent at point of tangency)
• ∠BOC = 54° (given)
• ∠OCB = x (what we need to find)

The sum of angles in a triangle is 180 degrees.

In △ OBC, ∠OBC + ∠BOC + ∠OCB = 180°

Substituting the known values:

90° + 54° + x = 180°

144° + x = 180°

x = 180° - 144°

x = 36°

Therefore, the value of x is 36 degrees.

Ответ: 36