Say there are two lines that are tangent to a circle at points A and B, so that they intersect at an external point C, as shown below.
Two congruent right triangles are formed, since the tangent line is perpendicular to the radius. So line AC has the same length as line BC.
If the angle ACB is known, how can the length of line AC be calculated?
For example, if the radius $r$ is 1, and the angle ACB is $60\unicode{xb0}$, what is the length of line AC?
$\endgroup$ 31 Answer
$\begingroup$If $\angle ACB=60$ then $\angle ACO=30$ and therefore $OC=2$. Now you can use pythagoras and find $AC$. Using pythagoras : $OC^2=OA^2+AC^2$ and you will have: $4=1+AC^2$ Therefore $AC=\sqrt 3$
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