#1**+1 **

Since BC bisects angle ABQ then angle ABC = angle CBQ = x

[Definition of an angle bisector ]

Since angle CBQ = x, then minor arc BC = 2x

[ A tangent meeting a chord forms an angle that is 1/2 the measure of the arc intercepted by the chord ]

Angle A = (1/2 ) minor arc BC = (1/2)(2x) = x

[ A is an inscribed angle....ts measure = 1/2 of its intercepted arc ]

Since angle A = angle ABC, the sides opposite these angles are also equal

So AC = BC

[ In a triangle.....sides opposite equal angles are also equal ]

CPhill Nov 29, 2018