Q: In AABC, F, D bisects EC and BC respectively, what will be the lengths of FC? A 9cm B 8cm C 6cm D 7cm

To find the lengths of $FC$ in triangle $AABC$ where $F$ and $D$ bisect $EC$ and $BC$ respectively, we can follow these steps:

1. Break Down the Problem

Identify the relationships given in the problem:

• $F$ bisects $EC$, meaning $EF = FC$.
• $D$ bisects $BC$, meaning $BD = DC$.

2. Relevant Concepts

The concept of a bisector implies that the two segments created by $F$ and $D$ are equal in length. This means: $EF = FC$ and $BD = DC$

3. Analysis and Detail

Let’s assign some variables to the lengths:

• Let $EC = x$. Since $F$ bisects $EC$, then: $EF = FC = \frac{x}{2}$

We also need to consider the total lengths and how they relate to possible provided answers. Since triangle dimensions are not provided, we cannot calculate specific numerical terms. However, we check against the given options which are $9 \text{ cm}, 8 \text{ cm}, 6 \text{ cm},$ and $7 \text{ cm}$.

4. Verify and Summarize

To find $FC$:

1. $FC$ can only be calculated if we know the total length $EC$.
2. Given the equal segments formed by the bisection, $FC$ would be half of $EC$.

Based on the options presented:

• If $EC = 18$ cm, $FC = 9$ cm.
• If $EC = 16$ cm, $FC = 8$ cm.
• If $EC = 12$ cm, $FC = 6$ cm.
• If $EC = 14$ cm, $FC = 7$ cm.

As no specific length for $EC$ is given, we will select potential answers based on common segment bisector results.

Final Answer

Based on given options, the lengths of $FC$ could be $9 \text{ cm}, 8 \text{ cm}, 6 \text{ cm},$ or $7 \text{ cm}$. Thus, without loss of generality in assignment, all options are conditionally possible based on the original length $EC$. Please clarify lengths or provide additional dimension information to select a definitive answer.