1965 IMO Problems/Problem 5
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Problem
Consider with acute angle . Through a point perpendiculars are drawn to and , the feet of which are and respectively. The point of intersection of the altitudes of is . What is the locus of if is permitted to range over (a) the side , (b) the interior of ?
Solution
Let . Equation of the line . Point . Easy, point . Point , . Equation of , equation of . Solving: . Equation of the first altitude: . Equation of the second altitude: . Eliminating from (1) and (2): a line segment . Second question: the locus consists in the .
See Also
1965 IMO (Problems) • Resources | ||
Preceded by Problem 4 |
1 • 2 • 3 • 4 • 5 • 6 | Followed by Problem 6 |
All IMO Problems and Solutions |