0

Can we determine the length of the tangents from an exterior point to the circle if only the raidius of the circle is known.

1 Answers1

0

As commented by David Quinn, if you have the following diagram for your circle and tangent:

Circle with Tangent

in addition to knowing the length of the radius $\overline{OX}$, you would also need to know the length of the segment $\overline{OD}$ (i.e., the distance from the center of the circle to the exterior point), in order to be able to compute the length of the segment $\overline{DX}$ via the Pythagorean theorem:

$$\overline{DX} = \sqrt{\overline{OD}^2 - \overline{OX}^2}.$$