Question

two tangents each intersect a circle at opposite endpoints of the same diameter. is it possible for the two tangents to intersect each other outside the circle? explain why or why not, using the information you learned in this lesson.

Explanation:

A tangent to a circle is perpendicular to the radius at the point of tangency. If two tangents touch a circle at the endpoints of a diameter, the radii to these points are in a straight line (the diameter), so each tangent is perpendicular to this diameter. Since two lines perpendicular to the same line are parallel, the two tangents are parallel. Parallel lines never intersect, so they can't intersect outside the circle.

Answer:

It is not possible for the two tangents to intersect each other outside the circle. A tangent to a circle is perpendicular to the radius at the point of tangency. For the two tangents at the endpoints of a diameter, the radii to these points form a straight line (the diameter), so each tangent is perpendicular to this diameter. Two lines perpendicular to the same line are parallel, and parallel lines do not intersect (including outside the circle).