Difference between revisions of "2016 JBMO Problems"
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| + | A trapezoid <math>ABCD</math> (<math>AB || CF</math>,<math>AB > CD</math>) is circumscribed.The incircle of the triangle <math>ABC</math> touches the lines <math>AB</math> and <math>AC</math> at the points <math>M</math> and <math>N</math>,respectively.Prove that the incenter of the trapezoid <math>ABCD</math> lies on the line <math>MN</math>. | ||
[[2016 JBMO Problems/Problem 1#Solution|Solution]] | [[2016 JBMO Problems/Problem 1#Solution|Solution]] | ||
Revision as of 00:40, 23 April 2018
Problem 1
A trapezoid 
(
,
) is circumscribed.The incircle of the triangle 
touches the lines 
and 
at the points 
and 
,respectively.Prove that the incenter of the trapezoid lies on the line 
.
Problem 2
Problem 3
Problem 4
See also
| 2016 JBMO (Problems • Resources) | ||
| Preceded by 2015 JBMO Problems |
Followed by 2017 JBMO Problems | |
| 1 • 2 • 3 • 4 | ||
| All JBMO Problems and Solutions | ||
