Question

if the length of $overline{ec}$ is 22, find the length of $overline{eq}$. a. 17 b. 22 c. 11 d. 15

Explanation:

Step1: Identify the relationship

We know that $EG$ is a diameter and $EQ + QG=EG$. Also, assume $EQ = x$, then $QG = 5$. And $EC$ is a chord and we are not using its length for this simple diameter - radius relationship problem. Since $EG$ is a diameter and $Q$ is the center (implied as mid - point of diameter), if we consider the relationship between the segments on the diameter, we have $EQ+QG$ where $QG = 5$.

Step2: Calculate $EQ$

Let $EQ=x$. We know that $x + 5$ is part of the diameter - related segments. But we made a wrong start above. Since $EC$ is likely a mis - written $EG$ (as there is no $C$ in the circle diagram). If $EG = 22$ and $Q$ is the center of the circle (mid - point of $EG$), then $EQ=\frac{EG}{2}$.
$EQ=\frac{22}{2}=11$

Answer:

C. 11