The question asks to find the length of CK, given MK = 17. The image shows a triangle MKC, with a line segment CD perpendicular to MK, and D is the midpoint of MK. Also, CD is a median and an altitude. Triangle MKC is an isosceles triangle with MC = CK. Since MK = 17, and D is the midpoint of MK, MD = DK = 17/2 = 8.5. In triangle CKD, CK^2 = CD^2 + DK^2. However, CD is not given. The problem states that MK = 17, CK = ?. There is a label '10' near the line segment CK, which might represent the length of CK. Assuming the '10' near CK is the length of CK, then CK = 10. If the question is asking for the length of CK, and there is a '10' labeled near CK, then the answer is 10. The problem also mentions that C is on the perpendicular bisector of MK, which means triangle MKC is isosceles with MC = CK. The label 10 is placed near CK. Let's assume that 10 is the length of CK. If MK = 17, and triangle MKC is isosceles with MC = CK, then CK = 10.

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