Question

Find the values of x and y using the given chord, secant , and tangent lengths.x=y=

Answer 1

Let's find the values of x and y.

Take the following steps:

Step 1:

Apply the equation below to find x

$x^2=2(2+10)$

Let's solve for x.

Apply distributive property:

$\begin{gathered} x^2=2(2)+2(10) \\ \\ x^2=4+20 \\ \\ x^2=24 \\ \\ \text{Take the square root of both sides:} \\ \sqrt[]{x^2}=\sqrt[]{24} \\ \\ x=4.9 \end{gathered}$

Step 2:

Apply the equation below to find the value of y

$x^2=4(4+y)$

Substitute 24 for x² and find the value y:

$\begin{gathered} 24=4(4+y)^{} \\ \\ 24=4(4)+4(y) \\ \\ 24=16+4y \\ \\ \text{Subtract 16 from both sides:} \\ 24-16=16-16+4y \\ \\ 8=4y \end{gathered}$

Divide both sides by 4:

$\begin{gathered} \frac{8}{4}=\frac{4y}{4} \\ \\ 2=y \\ \\ y=2 \end{gathered}$

Therefore, we have:

x = 4.9

y = 2

ANSWER:

x = 4.9