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 length of BE? 14 units 17 units 27 units 34 units
2 answers:
Answer:
The missing figure is attached down
The length of BE is 27 units ⇒ 3rd answer
Step-by-step explanation:
In circle A:
- ∠BAE ≅ ∠DAE
- 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
- The length of B E is 3 x minus 24 and the length of E D is x + 10
We need to find the length of BE
∵ AB and AD are radii in circle A
∴ AB ≅ AD
In Δs EAB and EAD
∵ ∠BAE ≅ ∠DAE ⇒ given
∵ AB = AD ⇒ proved
∵ EA = EA ⇒ common side in the two triangles
- Two triangles have two corresponding sides equal and the
including angles between them are equal, then the two
triangles are congruent by SAS postulate of congruence
∴ Δ EAB ≅ Δ EAD ⇒ SAS postulate of congruence
By using the result of congruence
∴ EB ≅ ED
∵ EB = 3 x - 24
∵ ED = x + 10
- Equate the two expressions to find x
∴ 3 x - 24 = x + 10
- Add 24 to both sides
∴ 3 x = x + 34
- Subtract x from both sides
∴ 2 x = 34
- Divide both sides by 2
∴ x = 17
Substitute the value of x in the expression of the length of BE to find its length
∵ BE = 3 x - 24
∵ x = 17
∴ BE = 3(17) - 24
∴ BE = 51 - 24
∴ BE = 27
The length of BE is 27 units
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