Difference between revisions of "1987 OIM Problems/Problem 6"
(Created page with "== Problem == Let <math>ABCD</math> be a planar convex quadrilateral, <math>P</math> and <math>QQ</math> are points of <math>AD</math> and <math>BC</math> respectively such th...") |
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<cmath>\frac{AP}{PD}=\frac{AB}{DC}=\frac{BQ}{QC}</cmath> | <cmath>\frac{AP}{PD}=\frac{AB}{DC}=\frac{BQ}{QC}</cmath> | ||
Prove that the angles that are formed between line <math>PQ</math> and lines <math>AB</math> and <math>DC</math> are equal. | Prove that the angles that are formed between line <math>PQ</math> and lines <math>AB</math> and <math>DC</math> are equal. | ||
| + | |||
| + | ~translated into English by Tomas Diaz. ~orders@tomasdiaz.com | ||
== Solution == | == Solution == | ||
{{solution}} | {{solution}} | ||
| + | |||
| + | == See also == | ||
| + | https://www.oma.org.ar/enunciados/ibe2.htm | ||
Latest revision as of 12:27, 13 December 2023
Problem
Let 
be a planar convex quadrilateral, 
and 
are points of 
and 
respectively such that:
![\[\frac{AP}{PD}=\frac{AB}{DC}=\frac{BQ}{QC}\]](http://latex.artofproblemsolving.com/5/f/d/5fd51a80cf4d97e0022bf5bddfb94e875038c495.png)
Prove that the angles that are formed between line 
and lines 
and 
are equal.
~translated into English by Tomas Diaz. ~orders@tomasdiaz.com
Solution
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