MathDB
fixed point

Source: Ireland 2007

July 6, 2009
geometrycircumcirclegeometric transformationreflectiongeometry proposed

Problem Statement

The point P P is a fixed point on a circle and Q Q is a fixed point on a line. The point R R is a variable point on the circle such that P,Q, P,Q, and R R are not collinear. The circle through P,Q, P,Q, and R R meets the line again at V V. Show that the line VR VR passes through a fixed point.
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