Study the diagram of circle V,
where two chords, JK¯¯¯¯¯¯¯¯
and LM¯¯¯¯¯¯¯¯¯,
are equidistant from the center.
Circle V as described in the problem. Segment of V to chord K J is marked congruent to segment of V to chord L M. If JK=3x+19
and LM=6x+7,
what is the length of segment JK?
Responses
4
4
15.5
15 point 5
31
31
24
24
3
To find the length of segment JK, we can set up an equation based on the fact that JK and LM are congruent.
Equation: 3x + 19 = 6x + 7
Solve for x:
3x - 6x = 7 - 19
-3x = -12
x = 4
Now, plug in x = 4 into either equation to find the length of JK:
JK = 3(4) + 19
JK = 12 + 19
JK = 31
Therefore, the length of segment JK is 31.