Question

page 16 of 17 Segments Inside a Circle Practice Complete this assessment to review what you’ve learned. It will not count toward your grade. 4 of 54 of 5 Items Question Use the image to answer the question. If △CDE has sides that are tangent to the circle, and CF=15 cm , BD=12 cm , and EG=4 cm , then what is the perimeter of △CDE ? (1 point) cm

Answer 1

To find the perimeter of triangle \( \triangle CDE \), we first need to understand that since the sides are tangent to the circle, the segments from the points of tangency to the vertices of the triangle have specific relationships.

From the information given, let’s assign the following variables based on the points of tangency:

- Let \( CE = CF \) which is given as \( 15 \, \text{cm} \).
- Let \( DE = DG \) which is the same length as the segment \( BD \) since they are tangent from the same external point (point D). Hence \( DE = 12 \, \text{cm} \).
- Let \( CD = CH \) which is the same length as segment \( EG \) since they are tangent from the same external point (point C). Hence \( CD = 4 \, \text{cm} \).

Now we can find the lengths of each side of the triangle:

1. \( CD = CE + EG = 15 + 4 = 19 \, \text{cm} \)
2. \( DE = DF + BD = 15 + 12 = 27 \, \text{cm} \)
3. \( CE = CF + CH = 15 + 4 = 19 \, \text{cm} \)

Now we can substitute the values into the perimeter formula, which is the sum of all the sides:

\[
\text{Perimeter} = CD + DE + CE
\]
\[
= 19 \, \text{cm} + 27 \, \text{cm} + 19 \, \text{cm}
\]

Now, calculate the total:

\[
\text{Perimeter} = 19 + 27 + 19 = 65 \, \text{cm}
\]

So, the perimeter of triangle \( \triangle CDE \) is \( 65 \, \text{cm} \).