Answer:
AD = 27 units
Explanation:
In the above question, we have a circumscribed Polygon, were circle XYZ is inside the polygon ABCD
We were given the following side
AB=21 units
BC=24 units
CD=30 units
Side AB = AW + BW
21 units = x + 21 - x
Side BC = BX + CX
BX = BW , hence BX = 21 - x
Side BC = 21 units
24 = 21 - x + CX
CX = 24 - (21 - x)
CX = 24 - 21 + x
CX = 3 + x
Side CD = CY + DY
Note that: CY = CX, hence, CY = 3 + x
Side CD = 30 units
30 = 3 + x + DY
DY = 30 - (3 + x)
DY = 30 - 3 - x
DY = 27 - x
Side AD = AZ + DZ
Note also that:
AZ = AW , hence AZ = x
DY = DZ , hence DZ = 27 - x
Side AD = x + 27 - x
Side AD = 27 units