NOTE: Please WAIT while the applet below loads.
The sketch below illustrates part of a dynamic proof of the Klingens-Lux problem, which can be formulated as follows:
Let c1 and c2 be two circles intersecting in A and B and a straight line through A is drawn, intersecting the two circles in M and N. Further let K be the midpoint of MN, P the intersection point of the angle bisector of ∠MAB with c1, R the intersection point of the angle bisector of ∠ BAN with c2. Prove that ∠ PKR = 90o.
Drag the point M on circle c1 in the direction of A, and observe what happens.
Klingens-Lux Dynamic Proof
Challenge:
Can you explain why (prove that) your observation above is true?
Downloadable Geogebra & Sketchpad sketches
To download a zipped file containing both dynamic sketches above, Click Here.
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Created 31 March 2020 by Michael de Villiers.