Two tangents to a circle from the same external points are equal. This means that
QR = QX
SR = ST
UT = UV
WV = WX
From the diagram,
UV = 9
thus, UT = 9
ST + UT = 15
ST + 9 = 15
ST = 15 - 9
ST = 6
Thus, SR = 6
The perimeter of a figure is the distance around it. Thus, perimeter of the given figure is
Perimeter = QS + SU + UW + QW
QS = 19 + 6 = 25
SU = 15
UW = 9 + 9 = 18
QW = 9 + 19 = 28
Thus,
perimeter = 25 + 15 + 18 + 28
perimeter = 86