Question

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
△
𝐶
𝐷
𝐸
has sides that are tangent to the circle, and CF=15 cm
𝐶
𝐹
=
15

cm
, BD=12 cm
𝐵
𝐷
=
12

cm
, and EG=4 cm
𝐸
𝐺
=
4

cm
, then what is the perimeter of △CDE
△
𝐶
𝐷
𝐸
?

(1 point)
cm

Answer 1

For an incircle, tangents from the same vertex are equal. Thus
- CB = CF = 15,
- DB = DG = 12,
- EG = EF = 4.

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

Perimeter = 27 + 16 + 19 = 62 cm.