Question

ch. 5.1 - perpendicular and angle bisectors mix - assignment
find the length of \\( \overline { c a } \\) in the figure below.
*** just type the number and nothing else.
\\( c d = \\)

Explanation:

Step1: Use the perpendicular bisector theorem

Since \(BD\) is the perpendicular bisector of \(AC\), by the perpendicular bisector theorem, \(CD = AD\). So, \(2x + 4=4x\).

Step2: Solve the equation for \(x\)

Subtract \(2x\) from both sides of the equation \(2x + 4=4x\). We get \(4x-2x=4\), which simplifies to \(2x = 4\). Then divide both sides by \(2\), \(x=\frac{4}{2}=2\).

Step3: Find the length of \(CD\)

Substitute \(x = 2\) into the expression for \(CD\). \(CD=2x + 4\). Plugging in \(x = 2\), we have \(CD=2\times2+4\). First, calculate \(2\times2 = 4\), then \(4 + 4=8\).

Answer:

8