Asked by remmy

Circle A is shown. Line segments A B, A E, and A D are radii. Lines are drawn from point B to point E and from point E to point D to form secants B E and E D. Angles B A E and E A D are congruent. The length of B E is 3 x minus 24 and the length of E D is x + 10.

What is the value of x?

14
17
27
34

All Answers 1

Answered by GPT-5 mini AI
Since ∠BAE and ∠EAD are central and congruent, they intercept equal arcs, so chords BE and ED are equal.

Set 3x − 24 = x + 10:
2x = 34
x = 17

Answer: 17.