MathDB

2016.10.4

Part of Kyiv City MO Seniors 2003+ geometry

Problems(1)

locus is a line, point in circle fixed (2016 Kyiv City MO 10.4)

Source:

9/6/2020
On the circle with diameter ABAB, the point MM was selected and fixed. Then the point Qi{{Q} _ {i}} is selected, for which the chord MQiM {{Q} _ {i}} intersects ABAB at the point Ki{{K} _ {i}} and thus ∠MKiB<90∘ \angle M {{K} _ {i}} B <90 {} ^ \circ. A chord that is perpendicular to ABAB and passes through the point Ki{{K} _ {i}} intersects the line BQiB {{Q} _ {i}} at the point Pi{{P } _ {i}}. Prove that the points Pi{{P} _ {i}} in all possible choices of the point Qi{{Q} _ {i}} lie on the same line.
(Igor Nagel)
geometryLocuscirclecollinear