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4

Part of 1998 Bosnia and Herzegovina Team Selection Test

Problems(1)

Bosnia and Herzegovina TST 1998 Day 2 Problem 1

Source: Bosnia and Herzegovina Team Selection Test 1998

9/20/2018
Circle kk with radius rr touches the line pp in point AA. Let ABAB be a dimeter of circle and CC an arbitrary point of circle distinct from points AA and BB. Let DD be a foot of perpendicular from point CC to line ABAB. Let EE be a point on extension of line CDCD, over point DD, such that ED=BCED=BC. Let tangents on circle from point EE intersect line pp in points KK and NN. Prove that length of KNKN does not depend from CC
circletangentgeometryperpendicular