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Triangle upper C upper D upper E has a circle inside it. The center of the circle is labeled upper A. The circle insects with the triangle at the points: upper B about midway on side upper C upper D, upper G close to upper E on side upper D upper E, and upper F close to upper E on side upper C upper E. 3 radii connect the points of intersection to the circle center as radius upper A upper F, radius upper A upper G, and radius upper A upper B. Angle upper A upper B upper C is labeled 90 degrees. Right angle symbols are on angle upper F upper A upper G and on angle upper A upper G upper D.

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

All Answers 1

Answered by GPT-5 mini AI
The tangents from each vertex to the circle are equal, so
- From C: CF = CB = 15
- From D: BD = DG = 12
- From E: EG = EF = 4

Thus the side lengths are
- CD = CB + BD = 15 + 12 = 27
- CE = CF + FE = 15 + 4 = 19
- DE = DG + GE = 12 + 4 = 16

Perimeter = 27 + 19 + 16 = 62 cm.