Question

find the measure of the red chord.
the measure of the red chord is \boxed{}.

Explanation:

Step1: Set segments equal

A radius perpendicular to a chord bisects the chord, so $x+5=2x+6$

Step2: Solve for x

Subtract $x$ and 6 from both sides:
$x+5 - x -6 = 2x+6 - x -6$
$-1 = x$

Step3: Find one segment length

Substitute $x=-1$ into $x+5$:
$(-1)+5=4$

Step4: Calculate full chord length

The chord is twice the segment length:
$2\times4=8$

Answer:

8