Difference between revisions of "1967 AHSME Problems/Problem 32"
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<math>\sqrt{166}</math> | <math>\sqrt{166}</math> | ||
| + | After drawing the diagram, we see that we actually have a lot of lengths to work with. Considering triangle ABD, we know values of <math>AB, BD(BD = BO + OD)</math>, but we want to find the value of AD. We can apply stewart's theorem now, letting <math>m = 4, n = 6, AD = X, AB = 6</math>, and we have <math>10 \cdot 6 \cdot 4 + 8 \cdot 8 \cdot 10 = x^2 + 36 \cdot 6</math>, and we see that <math>x = \sqrt{166}</math>, <math>\boxed{E \sqrt{166}}</math> | ||
== See also == | == See also == | ||
{{AHSME box|year=1967|num-b=31|num-a=33}} | {{AHSME box|year=1967|num-b=31|num-a=33}} | ||
Revision as of 17:18, 10 September 2020
In quadrilateral 
with diagonals 
and 
, intersecting at 
, 
, 
, 
, 
, and 
. The length of 
is:
After drawing the diagram, we see that we actually have a lot of lengths to work with. Considering triangle ABD, we know values of 
, but we want to find the value of AD. We can apply stewart's theorem now, letting 
, and we have 
, and we see that 
, 
See also
| 1967 AHSME (Problems • Answer Key • Resources) | ||
| Preceded by Problem 31 |
Followed by Problem 33 | |
| 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 | ||
| All AHSME Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
