Difference between revisions of "2006 Seniors Pancyprian/2nd grade/Problem 4"
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== Problem == | == Problem == | ||
| − | A quadrilateral <math> | + | A quadrilateral <math>ABCD</math>, that has no parallel sides, is inscribed in a circle, its sides <math>DA</math>, <math>CB</math> meet at <math>E</math> and its sides <math>BA</math>, <math>CD</math> meet at <math>Z</math>. |
| − | If the bisectors of of <math>\angle | + | If the bisectors of of <math>\angle DEC</math> and <math>\angle CZB</math> intersect the sides of the quadrilateral at the points <math>K , L, M ,N</math> prove that |
| − | i) | + | i)The bisectors intersect normally |
| − | ii)the points <math> | + | ii)the points <math>K , L, M ,N</math> are vertices of a rhombus. |
== Solution == | == Solution == | ||
Latest revision as of 00:10, 20 February 2020
Problem
A quadrilateral 
, that has no parallel sides, is inscribed in a circle, its sides 
, 
meet at 
and its sides 
, 
meet at 
.
If the bisectors of of 
and 
intersect the sides of the quadrilateral at the points 
prove that
i)The bisectors intersect normally
ii)the points are vertices of a rhombus.
