Difference between revisions of "1965 AHSME Problems/Problem 37"
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<cmath>\frac{\text{m} C}{\text{m} E} + \frac{\text{m} D}{\text{m} A} = \frac{2}{4} + \frac{3}{3} = \frac{1}{2} + 1 = \frac{3}{2}</cmath> | <cmath>\frac{\text{m} C}{\text{m} E} + \frac{\text{m} D}{\text{m} A} = \frac{2}{4} + \frac{3}{3} = \frac{1}{2} + 1 = \frac{3}{2}</cmath> | ||
− | This answer corresponds to | + | This answer corresponds to <math>\fbox{\textbf{(C)}}</math>. |
~JustinLee2017 | ~JustinLee2017 |
Revision as of 08:53, 20 July 2024
Problem
Point is selected on side
of
in such a way that
and point
is selected on side
such that
. The point of intersection of
and
is
. Then
is:
Solution
We use mass points for this problem. Let denote the mass of point
.
Rewrite the expression we are finding as
Now, let
. We then have
, so
, and
We can let
. We have
From here, substitute the respective values to get
This answer corresponds to
.
~JustinLee2017
See Also
1965 AHSC (Problems • Answer Key • Resources) | ||
Preceded by Problem 36 |
Followed by Problem 38 | |
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 | ||
All AHSME Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.