MathDB

7

Part of 2014 Korea Junior Math Olympiad

Problems(1)

Menelaus and Length Bashing

Source: Korean National Junior Olympiad Number 7

11/2/2014
In a parallelogram □ABCD\Box ABCD (AB<BC)(AB < BC) The incircle of △ABC\triangle ABC meets BC‾\overline {BC} and CA‾\overline {CA} at P,QP, Q. The incircle of △ACD\triangle ACD and CD‾\overline {CD} meets at RR. Let SS = PQPQ ∩\cap ADAD UU = ARAR ∩\cap CSCS TT, a point on BC‾\overline {BC} such that AB‾=BT‾\overline {AB} = \overline {BT}
Prove that AT,BU,PQAT, BU, PQ are concurrent
geometryparallelogramincenterrhombusprojective geometrygeometry unsolved