Point z is the circumcenter of δlmn.

which must be true?

bmz cmz
zbm zcm

we know that

The circumcenter is the center of the the circle that passes through all three of the triangle's vertices.  Is the point of intersection of perpendicular bisectors of three sides of the triangle

so

-----> is equal to the radius of the circle  that passes through all three of the triangle's vertices

In this problem

m∠ZBM=

m∠ZCM=

therefore

m∠ZBM=m∠ZCM -----> is true-

the answer is the option

m∠ZBM=m∠ZCM

step-by-step explanation: