MathDB
Tangent Circles

Source: OMM 2010 3

July 15, 2014
geometry

Problem Statement

Let C1\mathcal{C}_1 and C2\mathcal{C}_2 be externally tangent at a point AA. A line tangent to C1\mathcal{C}_1 at BB intersects C2\mathcal{C}_2 at CC and DD; then the segment ABAB is extended to intersect C2\mathcal{C}_2 at a point EE. Let FF be the midpoint of \overarc{CD} that does not contain EE, and let HH be the intersection of BFBF with C2\mathcal{C}_2. Show that CDCD, AFAF, and EHEH are concurrent.