a) since <BXC is 90 deg, B, X, C lie on semi-circle, diameter BC, centre M. .: BM = MC = MX, being radii of this semi-circle.
b) since BM = MX, MBX is an isosceles triangle. So base angles MBX and MXB are equal = @ say.
c) .: <DAC = <DBC = @
and < CXM = 90 - < MXB = 90 - @...