MathDB

1

Part of 2003 Kurschak Competition

Problems(1)

Power of a point practise

Source: Kürschák 2003, problem 1

7/8/2014
Draw a circle kk with diameter EF‾\overline{EF}, and let its tangent in EE be ee. Consider all possible pairs A,B∈eA,B\in e for which E∈AB‾E\in \overline{AB} and AE⋅EBAE\cdot EB is a fixed constant. Define (A1,B1)=(AF∩k,BF∩k)(A_1,B_1)=(AF\cap k,BF\cap k). Prove that the segments A1B1‾\overline{A_1B_1} all concur in one point.
geometrycircumcirclegeometry unsolved