MathDB

Let

ABCD

be a rectangle with

AB=a >CD =b

. Given circles

(K_1,r_1) , (K_2,r_2)

with

r_1<r_2

tangent externally at point

K

and also tangent to the sides of the rectangle, circle

(K_1,r_1)

tangent to both

AD

and

AB

, circle

(K_2,r_2)

tangent to both

AB

and

BC

. Let also the internal common tangent of those circles pass through point

D

. (i) Express sidelengths

a

and

b

in terms of

r_1

and

r_2

. (ii) Calculate the ratios

\frac{r_1}{r_2}

and

\frac{a}{b}

. (iii) Find the length of

DK

in terms of

r_1

and

r_2

Problem Statement