Difference between revisions of "1971 Canadian MO Problems"
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== Problem 2 == | == Problem 2 == | ||
| − | + | Let <math>x</math> and <math>y</math> be positive real numbers such that <math>x+y=1</math>. Show that <math>\left(1+\frac{1}{x}\right)\left(1+\frac{1}{y}\right)\ge 9</math>. | |
[[1971 Canadian MO Problems/Problem 2 | Solution]] | [[1971 Canadian MO Problems/Problem 2 | Solution]] | ||
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| − | + | <math>ABCD</math> is a quadrilateral with <math>AD=BC</math>. If <math>\angle ADC</math> is greater than <math>\angle BCD</math>, prove that <math>AC>BD</math>. | |
[[1971 Canadian MO Problems/Problem 3 | Solution]] | [[1971 Canadian MO Problems/Problem 3 | Solution]] | ||
Revision as of 21:27, 13 December 2011
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Contents
Problem 1
is a chord of a circle such that 
and 
Let 
be the center of the circle. Join 
and extend to cut the circle at 
Given 
find the radius of the circle
Problem 2
Let 
and 
be positive real numbers such that 
. Show that 
.
Problem 3
is a quadrilateral with 
. If 
is greater than 
, prove that 
.
Problem 4
Determine all real numbers 
such that the two polynomials 
and 
have at least one root in common.
