Question

in the figure below, c is between a and d, and b is the mid - point of $overline{ac}$. if $bd = 14$ and $bc = 8$, find $ad$.

Explanation:

Step1: Find the length of CD

Since $BD = 14$ and $BC = 8$, then $CD=BD - BC$.
$CD = 14 - 8=6$.

Step2: Find the length of AC

Because B is the mid - point of AC and $BC = 8$, then $AC = 2\times BC$.
$AC=2\times8 = 16$.

Step3: Find the length of AD

$AD=AC + CD$.
$AD=16 + 6=22$.

Answer:

22