Given: circles k1(a) and k2(o)ext. tangent
ke- tangent to k1(a) and k2(o)
ak=5, oe=4 find: ke

there is a visual

AO is a line segment containing the radii of both circles, which are AK and OE, so AO = AK + OE = 9.

Extend AO to a point P on the line KE. Then we get two similar triangles APK and OPE. Let be the length of KE, the length of EP, and the length of OP.

By similarity, we have

OPE is a right triangle, so

Now,

and we also have

Substituting this into the expression containing gives us an equation that we can solve for :

total = principal × ( 1 + rate ) ^ years

total = 600 * (1.04)^5

total = 729.99

answer is c

step-by-step explanation: