Question

in the figure below, s is the center of the circle. suppose that $jk = 20$, $lk = 3x + 2$, $sn = 12$, and $sp = 12$. find the following.
$x = \square$
$jn = \square$

Explanation:

Step1: Use chord perpendicular bisector theorem

A line from the center perpendicular to a chord bisects the chord. So $JN = \frac{JK}{2}$

Step2: Calculate JN value

Substitute $JK=20$:
$JN = \frac{20}{2} = 10$

Step3: Set equal chord distances, solve for x

Since $SN=SP=12$, chords $JK$ and $LK$ are congruent, so $LK=JK=20$. Set up equation:
$3x + 2 = 20$

Step4: Isolate and solve for x

Subtract 2 from both sides:
$3x = 20 - 2 = 18$
Divide by 3:
$x = \frac{18}{3} = 6$

Answer:

$x = 6$
$JN = 10$