Question

In the figure below S is the center of the circle. Suppose that JK = 2x-2, LK= 12, SN= 5 and SP= 5. Find x and PL.

Answer 1

Since the radius SR is perpendicular to the chord LK, it divides the chord in two segments with equal length, so we can find PL:

`\begin{gathered} LK=2\cdot PL \\ 2\cdot PL=12 \\ PL=6 \end{gathered}`

Since SN and SP have the same length, the chords LK and JK also have the same length, so:

`\begin{gathered} JK=LK \\ 2x-2=12 \\ 2x=14 \\ x=7 \end{gathered}`

So the value of x is 7.