Answer:
The perimeter of the polygon is 48
Step-by-step explanation:
Given: [tex]\angle B \cong \angle D[/tex]
Step 1: To find the the lengths of the polygon, the circle theorem states that, "Two tangents from an external point to a circle are always equal in length".
Thus, the length of the line segment [tex]A B=5+6=11[/tex]
The length of the line segment [tex]B C=6+7=13[/tex]
Since, [tex]\angle B \cong \angle D[/tex],
The length of the line segment [tex]C D=7+6=13[/tex]
The length of the line segment [tex]D A=5+6=11[/tex]
Step 2: To find the perimeter of the polygon, add the length of the line segment.
[tex]\begin{aligned}\text {Perimeter} &=A B+B C+C D+D A \\&=11+13+13+11 \\&=48\end{aligned}[/tex]
Thus, the perimeter of the polygon is 48.
