Given that AC and BD are chords, apply the Intersecting Chord Theorem to set up an equation and solve for x

x = 6

Step-by-step explanation:

Chord Theorem

In a circle if two chords intersected at a point inside it there are four segments created, two in each cord, the products of the lengths of the line segments on each chord are equal

∵ AC and BD are two chords in a circle

∵ AC and BD intersect each other at a point inside the circle

- That means the products of the segments in each chord

   are equal

∵ The segments of AC are (2x - ) and 4

∵ The segments of BD are x and (x - 4)

∴ (2x - ) × 4 = x × (x - 4)

- Simplify each side

∴ (2x)(4) - ( )(4) = (x)(x) - (x)(4)

∴ 8x - 36 = x² - 4x

- Subtract 4x from both sides

∴ - 36 = x² - 12x

- Add 36 to both sides

∴ 0 = x² - 12x + 36

- Switch the two sides

∴ x² - 12x + 36 = 0

Now let us factorize the left hand side into two factors

∵ x² = (x)(x)

∵ 36 = (-6)(-6)

∴ (x)(-6) + (x)(-6) = -6x + -6x = -12x ⇒ middle term

- That means the two factors are (x - 6) and (x - 6)

∴ The factors of x² - 12x + 36 are (x - 6) and (x - 6)

∴ (x - 6)(x - 6) = 0

- Equate the factor by 0

∵ x - 6 = 0

- Add 6 to both sides

∴ x = 6

step-by-step explanation: