Question

in the figure below, c is between a and d, and b is the mid - point of ac. if bc = 6 and bd = 13, find ad.

Explanation:

Step1: Find the length of $CD$

Since $BD = 13$ and $BC=6$, then $CD=BD - BC$. So $CD = 13 - 6=7$.

Step2: Find the length of $AC$

Because $B$ is the mid - point of $AC$ and $BC = 6$, then $AC = 2\times BC$. So $AC=2\times6 = 12$.

Step3: Find the length of $AD$

We know that $AD=AC + CD$. Substitute $AC = 12$ and $CD = 7$ into the formula. So $AD=12 + 7=19$.

Answer:

$19$