If two segments tangent to a circle share a common endpoint outside the circle, then the two segments are congruent.
48 in.
Practice makes perfect
Take a look at this quadrilateral circumscribing the circle. Let's begin by naming the vertices and points of tangency on the given diagram.
To find the perimeter of the quadrilateral, we need to find the length of CD. Recall that if two tangent segments to a circle share a common endpoint outside the circle, then the two segments are congruent. Using this fact, we can find the length of EF.
The length of EG is 14 inches. Therefore, we can find the length of FG by subtracting 8 from 14.
FG= 14- 8= 6in.
Now that we know the length of FG, we can use the same relationship between tangents to find the length of GH.
The length of GA is 13 inches. Therefore, the length of HA can be found by subtracting 6 from 13.
HA=13- 6= 7in.
Again, using the same relationship as before, we know that the length of AB is 7 as well.
Now, by subtracting 7 from 10, we find that the length of BC is 3 inches. We can again use the fact that if two segments tangent to a circle share a common endpoint, they are congruent. This tells us that the length of CD is also 3 inches.
Now that we know all the side lengths, we can find the perimeter of the circumscribed polygon by adding them.
&P= 8+ 8+ 6+ 6+ 7+ 7+ 3+ 3
&P=48 in.
