Question

in the figure below, c is between a and d, and b is the midpoint of $overline{ac}$. if $ad = 18$ and $bc = 5$, find $cd$.
image of a line segment with points a, b, c, d in order from left to right
$cd = \square$

Explanation:

Step1: Find AC since B is midpoint

Since B is the midpoint of \( \overline{AC} \), \( AB = BC = 5 \), so \( AC = AB + BC = 5 + 5 = 10 \).

Step2: Calculate CD using AD and AC

We know \( AD = AC + CD \), so \( CD = AD - AC \). Substituting \( AD = 18 \) and \( AC = 10 \), we get \( CD = 18 - 10 = 8 \).

Answer:

\( 8 \)