Question

1. in the diagram below, $overline{ab}$ and $overline{de}$ bisect each other. if $f$ is the mid - point of $overline{cd}$, $ab = 20$, and $de = 12$, then find the value of $fc+cb$. show how you arrived at your answer.

Explanation:

Step1: Use mid - point property

Since \(AB\) and \(DE\) bisect each other at \(C\), we know that \(AC = CB=\frac{AB}{2}\) and \(DC = CE=\frac{DE}{2}\). Given \(AB = 20\), then \(CB=\frac{20}{2}=10\). Given \(DE = 12\), and \(F\) is the mid - point of \(CD\), so \(CF=\frac{CD}{2}\), and \(CD=\frac{DE}{2} = 6\), then \(CF = 3\).

Step2: Calculate \(FC + CB\)

We want to find \(FC+CB\). Substitute the values of \(FC\) and \(CB\) we found above. \(FC + CB=3 + 10=13\).

Answer:

13