MathDB

3

Part of 1997 Balkan MO

Problems(1)

Two circles, externally tangent and a third circle comes in

Source: Balkan MO 1997, Problem 3

4/24/2006
The circles C1\mathcal C_1 and C2\mathcal C_2 touch each other externally at DD, and touch a circle ω\omega internally at BB and CC, respectively. Let AA be an intersection point of ω\omega and the common tangent to C1\mathcal C_1 and C2\mathcal C_2 at DD. Lines ABAB and ACAC meet C1\mathcal C_1 and C2\mathcal C_2 again at KK and LL, respectively, and the line BCBC meets C1\mathcal C_1 again at MM and C2\mathcal C_2 again at NN. Prove that the lines ADAD, KMKM, LNLN are concurrent. Greece
geometrygeometric transformationhomothetycircumcircleparallelogrampower of a point