Difference between revisions of "2016 JBMO Problems/Problem 1"
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== Problem == | == Problem == | ||
| − | A trapezoid <math>ABCD</math> (<math>AB || | + | A trapezoid <math>ABCD</math> (<math>AB || CD</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>. |
== Solution == | == Solution == | ||
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{{JBMO box|year=2016|before=First Problem|num-a=2|five=}} | {{JBMO box|year=2016|before=First Problem|num-a=2|five=}} | ||
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| + | [[Category:Intermediate Geometry Problems]] | ||
Latest revision as of 02:18, 3 March 2019
Problem
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 
.
Solution
See also
| 2016 JBMO (Problems • Resources) | ||
| Preceded by First Problem |
Followed by Problem 2 | |
| 1 • 2 • 3 • 4 | ||
| All JBMO Problems and Solutions | ||
