Question

in circle a, $angle bae cong angle dae$.
what is the length of $overline{be}$?
$\bigcirc$ 14 units
$\bigcirc$ 17 units
$\bigcirc$ 27 units
$\bigcirc$ 34 units
on the circle diagram: $overline{be}$ is labeled $3x - 24$, $overline{de}$ is labeled $x + 10$, center is point a, with points b, e, d on the circle

Explanation:

Step1: Set chords equal

Since $\angle BAE \cong \angle DAE$, the chords $\overline{BE}$ and $\overline{DE}$ are congruent. So:
$3x - 24 = x + 10$

Step2: Solve for x

Subtract $x$ from both sides:
$2x - 24 = 10$
Add 24 to both sides:
$2x = 34$
Divide by 2:
$x = 17$

Step3: Calculate length of $\overline{BE}$

Substitute $x=17$ into $3x-24$:
$3(17) - 24 = 51 - 24$

Answer:

27 units