MathDB

2

Part of 2008 Czech-Polish-Slovak Match

Problems(2)

Similar to Brianchon's Theorem

Source: Czech-Polish-Slovak 2008, P2

4/14/2013
ABCDEFABCDEF is a convex hexagon, such that ∣∠FAB∣=∣∠BCD∣=∣∠DEF∣|\angle FAB| = |\angle BCD| =|\angle DEF| and ∣AB∣=∣BC∣,|AB| =|BC|, ∣CD∣=∣DE∣|CD| = |DE|, ∣EF∣=∣FA∣|EF| = |FA|. Prove that the lines ADAD, BEBE and CFCF are concurrent.
geometrycircumcirclegeometry proposed
ABCDE- regualar pentagon. Find smallest value of expression

Source: Czech-Polish-Slovak 2008, P5

4/14/2013
ABCDEABCDE is a regular pentagon. Determine the smallest value of the expression ∣PA∣+∣PB∣∣PC∣+∣PD∣+∣PE∣,\frac{|PA|+|PB|}{|PC|+|PD|+|PE|}, where PP is an arbitrary point lying in the plane of the pentagon ABCDEABCDE.
geometry proposedgeometry