MathDB
The lines r,s,t and the two γ circles

Source:

November 21, 2010
geometry proposedgeometry

Problem Statement

Two circles γ1\gamma_1 and γ2\gamma_2 intersect at AA and BB. A line rr through BB meets γ1\gamma_1 at CC and γ2\gamma_2 at DD so that BB is between CC and DD. Let ss be the line parallel to ADAD which is tangent to γ1\gamma_1 at EE, at the smaller distance from ADAD. Line EAEA meets γ2\gamma_2 in FF. Let tt be the tangent to γ2\gamma_2 at FF. (a)(a) Prove that tt is parallel to ACAC. (b)(b) Prove that the lines r,s,tr,s,t are concurrent.
Back to ProblemsView on AoPS