1962 AHSME Problems/Problem 15
Problem
Given triangle with base fixed in length and position. As the vertex moves on a straight line, the intersection point of the three medians moves on:
Solution
Let be the median through vertex , and let be the point of intersection of the triangle's medians.
Let be the altitude of the triangle through vertex and be the distance from to , with the point laying on .
Using Thales' intercept theorem, we derive the proportion:
The fraction in any triangle is equal to . Therefore .
Since the problem states that the vertex is moving on a straight line, the length of is a constant value. That means that the length of is also a constant. Therefore the point is moving on a straight line.
Answer: D
See Also
1962 AHSC (Problems • Answer Key • Resources) | ||
Preceded by Problem 14 |
Followed by Problem 16 | |
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