Difference between revisions of "1960 IMO Problems/Problem 7"
(New page: ==Problem== An isosceles trapezoid with bases <math>a</math> and <math>c</math> and altitude <math>h</math> is given. a) On the axis of symmetry of this trapezoid, find all points <math>P...) |
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a) On the axis of symmetry of this trapezoid, find all points <math>P</math> such that both legs of the trapezoid subtend right angles at <math>P</math>; | a) On the axis of symmetry of this trapezoid, find all points <math>P</math> such that both legs of the trapezoid subtend right angles at <math>P</math>; | ||
| − | b) Calculate the distance of <math> | + | b) Calculate the distance of <math>P</math> from either base; |
c) Determine under what conditions such points <math>P</math> actually exist. Discuss various cases that might arise. | c) Determine under what conditions such points <math>P</math> actually exist. Discuss various cases that might arise. | ||
Revision as of 10:32, 16 February 2009
Problem
An isosceles trapezoid with bases 
and 
and altitude 
is given.
a) On the axis of symmetry of this trapezoid, find all points 
such that both legs of the trapezoid subtend right angles at ;
b) Calculate the distance of from either base;
c) Determine under what conditions such points actually exist. Discuss various cases that might arise.
Solution
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See Also
| 1960 IMO (Problems) • Resources | ||
| Preceded by Problem 6 |
1 • 2 • 3 • 4 • 5 • 6 | Followed by Last Question |
| All IMO Problems and Solutions | ||
