Need help for a geometric question

Question

AB is a diameter in a circle M,

AC and BD are two tangents of the circle M,

CM intersects the circle M at X and Y and intersects BD at E

Prove that : CX = YE

Answer 1

AB diameter of circle M -- Reason - Given

AC and BD tangent to circle M -- Reason - Given

CM intersects circle M at X, Y and BD at E -- Reason - Given

AB passes through midpoint M of circle M -- Reason - Definition of Diameter

AM congruent to BM -- Reason - Definition of Midpoint

AC perpendicular to AB, and BE Perpendicular to AB -- Reason - Tangent to a circle is perpendicular to diameter thm

Measure of angle CAB = 90 -- Reason - Definition of Perpendicular

Measure of angle EBA = 90 -- Reason - Definition of Perpendicular

angle CAB congruent to angle EBA -- Reason - Definition of Congruent Angles

Angle AMC congruent to angle BME -- Reason - Vertical Angles are Congruent

Triangle AMC congruent to triangle BME -- Reason - Angle Side Angle (ASA) congruence

CM congruent to EM -- Reason - Corresponding Sides of Congruent Triangles are Congruent

XM congruent to YM -- Reason - Definition of Radius

CM = CX + XM and EM = EY + YM -- Reason - Segment Addition

-XM - XM -YM - YM -- Reason - Subtraction Property of Equality

CX = XM - XM EY = EM - YM -- Reason - Reflexive Property

EY = CM - XM -- Reason - Substitution

CX = EY -- Reason - Substitution