Question

find the length of \\( \overline { c d } \\) in the figure below if \\( \overline { a c } \\) is a perpendicular bisector.
*** just type the number and nothing else.
\\( c d = \\)

Explanation:

Step1: Use the property of perpendicular bisector

Since \(AC\) is a perpendicular bisector, \(BC = DC\). So, \(10x - 4=4x + 14\).

Step2: Solve the equation for \(x\)

Subtract \(4x\) from both sides: \(10x-4x - 4=4x-4x + 14\), which gives \(6x-4 = 14\).
Add \(4\) to both sides: \(6x-4 + 4=14 + 4\), so \(6x=18\).
Divide both sides by \(6\): \(x=\frac{18}{6}=3\).

Step3: Find the length of \(CD\)

Substitute \(x = 3\) into \(4x + 14\). Then \(CD=4\times3+14=12 + 14=26\).

Answer:

26