Question

Please help me with this geometry problem. pls be fast when answering

Answer 1

Since both lines are tangent to the circle, we have that both have the same length, then, we can write the following equaiton:

`4x^2^{}+5x=5x+16`

solving for x, we get:

`\begin{gathered} 4x^2+5x=5x+16 \\ \Rightarrow4x^2+5x-5x=16 \\ \Rightarrow4x^2=16 \end{gathered}`

dividing both sides by 4, we get the following:

`\begin{gathered} (1)/(4)(4x^2=16) \\ \Rightarrow(4)/(4)x^2=(16)/(4) \\ \Rightarrow x^2=4 \\ \Rightarrow x=\pm\sqrt[]{4}=\pm2 \\ x=\pm2 \end{gathered}`

therefore, x = 2 or x = -2.