Question

In the figure below, the segments ST and SU are tangent to the circle centered at O. Given that OT = 13 and OS= 19.4, find SU.

Answer 1

`SU=6.2`

1) The best way to tackle this question is by keeping in mind some properties of tangent lines to a circle:

Since a tangent to a circle makes a 90º angle to the origin, we can trace another radius, and state that this is 13 units long. Therefore we have here two congruent triangles.

2) So, now if we find ST we'll find SU. So let's write a property that relates a tangent and a secant from one point

`\begin{gathered} SO^2=OT^2+ST^2 \\ (19.4)^2=(13)^2+ST^2 \\ 376.36=169+ST^2 \\ 376.36-169=ST^2 \\ ST^{}=\sqrt[]{38.36} \\ ST=6.19 \\ ST\cong SU \\ SU=6.2 \end{gathered}`