Question

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?

Answer 1

PQ "touching the circle" means PQ is the tangent.

_____
A tangent intersects a circle at exactly one point.

Answer 2

Answer:

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.