Question

if the length of $overline{bf}$ is 32 inches, what is the length of $overline{ch}$?
enter the answer in the space provided. use numbers instead of words.
inches box

Explanation:

Step1: Identify chord properties

In a circle, if a diameter is perpendicular to a chord, it bisects the chord. Also, chords equidistant from the center are equal in length. Here, $\overline{BF}$ and $\overline{EC}$ are both perpendicular to diameter $\overline{AD}$, so they are equal in length: $BF = EC = 32$ inches.

Step2: Bisect the chord $\overline{EC}$

Since $\overline{AD} \perp \overline{EC}$, $\overline{AD}$ bisects $\overline{EC}$. So $CH = \frac{1}{2}EC$.
<Expression>
$CH = \frac{1}{2} \times 32$
</Expression>

Step3: Calculate the length

Compute the value of $\frac{1}{2} \times 32$.
<Expression>
$CH = 16$
</Expression>

Answer:

16 inches