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In circle A, ∠BAE ≅ ∠DAE.

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
Because ∠BAE and ∠DAE are central and congruent, the intercepted arcs BE and ED (and therefore the chord lengths BE and ED) are equal. So

3x − 24 = x + 10
2x = 34
x = 17.

Answer: 17.