Point k divides the segment CP which is 2: 5. Find the length of the segment CK if CP = 21cm.

there are two options for events
1) SC more than CR
in this case, the ratio KR / SK = 2/5 from here 2SK = 5KR, we express from here KR KR = 2/5 SK;
SK + KR = SR = 21cm. (1)
we substitute the value of KR into equation (1) and find the SK
SC + 2 / 5SC = 21
7 / 5SC = 21
SK = 21 * 5/7 = 15 (see)

2) SK is less than KR
in this case, SK / KR = 2/5, in the same way we squeeze KP KR = 5 / 2SK;
again we substitute the value of KP in equation (1) and find the SK
SK + 5 / 2SC = 21
7 / 2SK = 21
SK = 21 * 2/7 = 6 (see)