Question

Circle D is shown. Line segment F E goes through point D. Line segment C D is shown. Line segment G H goes from one side of the circle to the other side. Line segment A B is outside of the circle and intersects the circle at point B.

In circle D, which is tangent to the circle?

Line G H
Line segment A B
CD
EF

Answer 1

Only line segment G H can be tangent to a circle, as it touches the circle at only one point. All other options intersect the circle at multiple points, making them chords or secants, not tangents.

In geometry, a tangent to a circle is a straight line that intersects the circle at exactly one point. This point of intersection is called the point of tangency.

Line segment A B: This line intersects the circle at two points, B and another point outside the circle, making it a secant.

CD: This line cuts through the circle at two points, C and D, making it a diameter (a special kind of secant that passes through the center of the circle).

EF: Similar to CD, this line intersects the circle at two points, E and F, making it a secant.

Line segment G H: This line touches the circle at only one point, H, making it a tangent.

Therefore, only line segment G H satisfies the definition of being a tangent to circle D. The other options, while intersecting the circle, do so at multiple points, disqualifying them from being tangents.