CRITICAL THINKING When will two lines tangent to the same circle not intersect? Justify your answer.
O The tangent lines will not intersect when they are external tangents.
○ This cannot happen; Two tangent lines must intersect at some point in the plane.
○ The tangent lines will not intersect when their points of tangency are different endpoints of the same diameter.
○ Two lines tangent to the same circle will not intersect when the two lines are not in the same plane.

Two lines tangent to the same circle will not intersect when they are external tangents. External tangents are lines that intersect the circle at different points but do not intersect each other within the circle itself. This scenario occurs when drawing tangent lines from a point external to the circle.

For example, if you draw two tangent lines to a circle from a point outside the circle, those tangent lines will be external tangents and will not intersect within the circle.

This situation is a unique case in which tangent lines to the same circle do not intersect, as typically, tangent lines intersect at a single point on the circle.

Learn more about Tangent lines to a circle here:

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