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
[tex]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[/tex]
Simplifying for the value of x , we get
[tex]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[/tex]
or, x = 3
Hence, the value of x = 3 units
