Question

In the circle below S is the center of the circle. Suppose that LM= 18, KN= 9, JN = 4x-3 and NS=5.5. Find x and PS.

Answer 1

We can note that KN=JN, which implies that

$4x-3=9$

then, by moving -3 to the right hand side, we get

$\begin{gathered} 4x=9+3 \\ 4x=12 \end{gathered}$

then, x is given by

$\begin{gathered} x=\frac{12}{4} \\ x=3 \end{gathered}$

that is, x is equal to 3.

Now, from the congruent chord theorem, we know that if 2 chords of a circle are congruent (as in our case because LM=JK), then they are equidistant form the center of the circle. In other words,

$NS=PS$

Therefore, PS measure 5.5 units.