Polygons that encircle a circle contain tangents of similar length, as such the perimeter of the polygon that circumscribes the circle is 76 cm.
What is circumscribing a circle inside a polygon?
The act of circumscribing a circle inside a polygon involves the process of drawing a circle that perfectly fits in the polygon by bisecting two arcs on each side of the polygon and then drawing a circle where all the sides meet in the middle of the polygon.
Polygons that encircle a circle contain tangents of similar length that originate at the same vertex, which explains the computation of the dimensions.
Taking a look at the figure attached, we have:
- Two tangents with a length of 19 cm
- Two tangents with a length of 9 cm
- Two tangents with a length of 4 cm
- Two tangents with with a length of 6 cm
Thus, the perimeter of the polygon can be calculated as:
= (19 + 19 + 6 + 6 + 4 + 4 + 9 + 9) cm
= 76 cm
Learn more about the perimeter of a polygon here:
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