Can we determine the length of the tangents from an exterior point to the circle if only the raidius of the circle is known.
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2You would need to know the distance from the centre to the exterior point – David Quinn May 21 '17 at 17:31
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Use pythogerous theorem then. Its a right angled triangle. – Vikranth Inti May 21 '17 at 17:32
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As commented by David Quinn, if you have the following diagram for your circle and 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:
$$\overline{DX} = \sqrt{\overline{OD}^2 - \overline{OX}^2}.$$
