MathDB

Let

C_1,C_2

and

C_3

be three pairwise disjoint circles. For each pair of disjoint circles, we define their internal tangent lines as the two common tangents which intersect in a point between the two centres. For each

i,j

, we define

(r_{ij},s_{ij})

as the two internal tangent lines of

(C_i,C_j)

. Let

r_{12},r_{23},r_{13},s_{12},s_{13},s_{23}

be the sides of

ABCA'B'C'

. Prove that

AA',BB'

and

CC'

are concurrent. https://cdn.artofproblemsolving.com/attachments/1/2/5ef098966fc9f48dd06239bc7ee803ce4701e2.png

Problem Statement