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Answer :
The length of LM segment in the circle M is equal to 16 cm.
In any circle, the diameter is twice the radius hence given diameter of circle M as 72cm then its radius KM is 36cm, and for circle J with diameter 58cm, its radius JL is 29cm.
To evaluate for the segment LM, we use the following equations;
KL + LM = KM
KL + LM = 36cm...(1)
KL + JK = JL
KL + JK = 29cm...(2)
Since JK = 9, equation (2) becomes;
KL + 9cm = 29cm
KL = 29cm - 9cm
KL = 20cm
substituting 20cm for KL in equation (1) we get;
20cm + LM = 36cm
LM = 36cm - 20cm
LM = 16cm.
Thus, the segment LM for the circle M is derived to be 16 centimeters.
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