Difference between revisions of "1957 AHSME Problems/Problem 26"

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== Solution ==
 
== Solution ==
<math>\fbox{\textbf{(E) the intersection of the medians of the triangle}}</math>.
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<math>\fbox{\textbf{(E) }the intersection of the medians of the triangle}</math>.
  
 
== See Also ==
 
== See Also ==

Revision as of 15:36, 25 July 2024

Problem

From a point within a triangle, line segments are drawn to the vertices. A necessary and sufficient condition that the three triangles thus formed have equal areas is that the point be:

$\textbf{(A)}\ \text{the center of the inscribed circle} \qquad \\  \textbf{(B)}\ \text{the center of the circumscribed circle}\qquad\\  \textbf{(C)}\ \text{such that the three angles formed at the point each be }{120^\circ}\qquad\\  \textbf{(D)}\ \text{the intersection of the altitudes of the triangle}\qquad\\  \textbf{(E)}\ \text{the intersection of the medians of the triangle}$

Solution

$\fbox{\textbf{(E) }the intersection of the medians of the triangle}$.

See Also

1957 AHSC (ProblemsAnswer KeyResources)
Preceded by
Problem 25
Followed by
Problem 27
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50
All AHSME Problems and Solutions

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