The value of x is 2 and the length of JK is 4
How to solve the unknown variables?
The given parameters from the circle are:
- Center = Point S
- Segment JK = 8
- Segment LK = 2x + 4
- Congruent SN = SP = 7
The lines SR and SQ are the radii of the circle P
This means that lines JK and JL are congruent
So, we have:
JK = KL
Substitute LK = 2x + 4 and JK = 4
4 = 2x + 4
Rewrite the above equation as:
2x + 4 = 8
Subtract 4 from both sides
2x + 4 - 4 = 8 - 4
Evaluate the difference
2x = 4
Divide both sides by 2
2x = 4/2
This gives
x = 2
Substitute x = 2 in LK = 2x + 4
LK = 2*2 + 4
Evaluate the product of 2 and 2
LK = 4 + 4
This gives
LK = 8
The point N divides JK into 2 equal segments
So, we have
JN = JK/2
JN= 8/2
JN = 4
Hence, the value of x is 2 and the length of JK is 4
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