Final answer:
Triangle ABC is a right triangle because BC is tangent to circle A, forming a 90-degree angle with the radius at the point of tangency.
Step-by-step explanation:
If line segment BC is tangent to circle A at point B, then triangle ABC must be a right triangle. This is because a tangent to a circle forms a 90-degree angle with the radius of the circle at the point of tangency. In this context, line segment AB would be the radius of the circle, and angle ABC would be a right angle. We can refer to the Pythagorean theorem, which relates to right triangles. It states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides (a² + b² = c²). Because we know one angle is 90 degrees, the sum of the other two angles must be 90 degrees as well (since the sum of angles in a triangle is always 180 degrees), making ABC a right triangle.