Look at the figure below: a circle is shown with the center o. or is a segment joining center o to a point r on the circle. pq is a line touching the circle in point r. line mn is shown intersecting the circle in points s and t. which is the tangent to the circle?

PAis tangent.

Step-by-step explanation:

Given that  A circle is shown with the center O. OR is a segment joining center O to a point R on the circle. PQ is a line touching the circle in Point R. Line MN is shown intersecting the circle in points S and T.

Since given that PQ is a line touching the circle in point R we have points P, Q and R are collinear.

PR, PQ or RQ is the tangent to the circle

MN is not a tangent since MN intersects the circle at two points S and T.

A tangent will not cut the circle at two points but meet the circle at only one point.

Hence PQ is the tangent.