Answer:
The perimeter of the polygon is 48 cm.
Step-by-step explanation:
Given: [tex]\angle B \cong \angle D[/tex]
To find the perimeter of the polygon, we need to find the lengths of the AB, BC, CD and DA
Since, [tex]\angle B \cong \angle D[/tex] and to find the length, from circle theorem, "Two tangents from an external point to a circle are always equal in length".
From this statement we shall conclude,
The length of [tex]AB=5+6=11[/tex]
The length of [tex]BC=6+7=13[/tex]
The length of [tex]CD=7+6=13[/tex]
The length of [tex]DA=6+5=11[/tex]
Thus, the perimeter of the polygon is
[tex]\begin{aligned}\text {Perimeter} &=A B+B C+C D+D A \\&=11+13+13+11 \\&=48 \mathrm{cm}\end{aligned}[/tex]
Hence, the perimeter of the polygon is 48 cm.
