Answer:
The correct option is C.
Step-by-step explanation:
It is given that CD is the perpendicular bisector of both XY and ST, and CY=20.
In triangle XCD and YCD,
[tex]CD=CD[/tex] (Common sides)
[tex]\angle XDC=\angle YDC=90^{\circ}[/tex] (Definition of perpendicular bisector)
[tex]\angle XD=\angle YD[/tex] (Definition of perpendicular bisector)
By SAS postulate of congruent triangles,
[tex]\triangle XCD=\triangle YCD[/tex]
The corresponding parts of congruent triangle are congruent,
[tex]CX=CY[/tex] (CPCTC)
[tex]XC=20[/tex] (CY=20)
The length of CX is 20 units. Therefore the correct option is C.
