Question

cr sem b geometry
special segments
the circle is inscribed in triangle aec.
which are congruent line segments? choose two correct answers.
\\(\overline{af}\\) and \\(\overline{ef}\\)
\\(\overline{cb}\\) and \\(\overline{cd}\\)
\\(\overline{ed}\\) and \\(\overline{cd}\\)
\\(\overline{ef}\\) and \\(\overline{ed}\\)

Explanation:

Step1: Recall Tangent Segment Theorem

Tangent segments from a common external point to a circle are congruent.

Step2: Analyze Each Option

• For $\overline{AF}$ and $\overline{EF}$: $A$ and $E$ are different external points, so no guarantee.
• For $\overline{CB}$ and $\overline{CD}$: $C$ is external point, $CB$ and $CD$ are tangents to the circle, so by theorem, $CB \cong CD$.
• For $\overline{ED}$ and $\overline{CD}$: $E$ and $C$ are different, no guarantee.
• For $\overline{EF}$ and $\overline{ED}$: $E$ is external point, $EF$ and $ED$ are tangents, so $EF \cong ED$.

Answer:

B. $\overline{CB}$ and $\overline{CD}$, D. $\overline{EF}$ and $\overline{ED}$ (assuming options are labeled as A: $\overline{AF}$ and $\overline{EF}$, B: $\overline{CB}$ and $\overline{CD}$, C: $\overline{ED}$ and $\overline{CD}$, D: $\overline{EF}$ and $\overline{ED}$)