Question

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

Answer 1

Answer:

The value of x  = 3 units

Step-by-step explanation:

Here, AC  = 3 ,( 5x - 3)

         BD = x , (x +9)

INTERSECTING CHORD THEOREM

It states that the products of the lengths of the line segments on each chord are equal.

Applying the theorem here, we get

$3( 5x - 3 ) = x (x +9)\\\implies 3(5x) - 3(3) = x(x) + 9 (x)\\or, 15x - 9= x^2 + 9x\\\implies x^2 + 9x - 15 x + 9 = 0\\or, x^2 -6x + 9 = 0$

Simplifying for the value of x , we get

$x^2 -6x + 9 = 0 \implies x^2 - 3x - 3x + 9 = 0\\x(x-3) -3(x -3) =0\\or, (x-3)(x-3) = 0$

or, x = 3

Hence, the value of x  = 3 units