Question

I need help on these questions on tangents and sectants

Answer 1

40.

We have to use the two-tangent theorem, to solve this.

The Two-Tangent Theorem states that if two tangent segments are drawn to one circle from the same external point, then they are congruent.

So, we can say:

`\begin{gathered} 2x^2+5=13 \\ \end{gathered}`

We can now solve this for x:

`\begin{gathered} 2x^2+5=13 \\ 2x^2=13-5 \\ 2x^2=8 \\ x^2=(8)/(2) \\ x^2=4 \\ x=\pm\sqrt[]{4} \\ x=2 \\ x=-2 \end{gathered}`