Question

Solve for x.

thanks!! ​

Answer 1

`x=3`

Explanation:

Use the Intersecting Chords Theorem to solve for x:

`\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`

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

Answer 2

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