Respuesta :
Answer:
x = 2
Step-by-step explanation:
Given 2 intersecting chords, then the product of the parts of one chord is equal to the product of the parts of the other chord, that is
EB × AE = ED × CE
x(x + 1) = 3 × 2 = 6
x² + x = 6 ( subtract 6 from both sides )
x² + x - 6 = 0 ← in standard form
(x + 3)(x - 2) = 0 ← in factored form
Equate each factor to zero and solve for x
x + 3 = 0 ⇒ x = - 3
x - 2 = 0 ⇒ x = 2
But x > 0 , then x = 2
The value of x is 2.
What is a Circle?
'Circle is a set of all points on a plane that are a fixed distance from a center.'
What is a Chord?
'A chord is the line segment joining two points on a curve.'
According to the given problem,
AE = x+1
EB = x
CE = 2ED = 3
We know,
When chords intersect inside a circle, the product of segment formed by the circle are equal.
Therefore,
(AE)*(EB)=(CE)*(ED)
⇒ (x+1) * x = 2 * 3
⇒ x² + x = 6
⇒ x² + x - 6 = 0
This is a quadratic equation,
Solving for x,
⇒ x² + 3x - 2x - 6 = 0
⇒ x( x + 3) - 2( x + 3) = 0
⇒ (x + 3)(x - 2) = 0
⇒ x = -3 , 2
We know that a chord length cannot be negative.
⇒ x = 2AE = 3 and EB = 2 , AB ⇒ ( 3+2 ) = 5
Hence, we can conclude the value of x is 2 and the length of the chord AB is 5.
Learn more about circles and chords here:
https://brainly.com/question/1654080
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