Respuesta :

Answer:

[tex]x=3[/tex]

Step-by-step explanation:

Use the Intersecting Chords Theorem to solve for x:

[tex]\overline{\rm TP}\cdot\overline{\rm PR}=\overline{\rm QP}\cdot\overline{\rm PS}\\\\(x+3)(x)=(6-x)(2x)\\\\x^2+3x=12x-2x^2\\\\3x^2+3x=12x\\\\3x^2-9x=0\\\\3x(x-3)=0\\\\x=0,\: x=3[/tex]

The solution [tex]x=0[/tex] however, does not make sense because the chords have lengths, so [tex]x=3[/tex] is the only sensible answer.

fieryanswererft

Intersecting Chords Theorem States:

  • |QP| * |PS| = |TP| * |PR|
  • |6-x| * |2x| = |x+3| * |x|
  • 12x -2x² = x² + 3x
  • -2x² -x² = 3x -12x
  • -3x² + 9x = 0
  • -3x(x -3) = 0
  • x - 3 = 0, -3x = 0
  • x = 3, 0

As Length cannot be zero or negative here. x = 3

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