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Given: AB is the perpendicular bisector of line IK
Angle IAK is a right angle
BI=BK
B is the midpoint of line IK<--
BK=AK

Answer 1

B is not on the line IK, so it cannot be the mid-point.

this one is more tricky. You know IJ=JK (because J is the mid point of line segment IK)
you know angle IJB = right angle (formed by perpendicular bisector AB)
also, angle KJB = right angle
so angle IJB = KJB
finally, JB= JB (a thing is equal to itself)

put that together and you have side-angle-side, for the triangles
IJB and KJB
which means their corresponding sides are congruent.

Answer 2

So BI=BK?

Answer 3

yes

Answer 4

Awesome thanks :)!