Difference between revisions of "1958 AHSME Problems/Problem 42"
Pateywatey (talk | contribs) (→Solution) |
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<cmath>(\sqrt{144 - h^2} - \sqrt{64 - h^2})(\sqrt{144 - h^2} + \sqrt{64 - h^2}) = 8(ED)</cmath> | <cmath>(\sqrt{144 - h^2} - \sqrt{64 - h^2})(\sqrt{144 - h^2} + \sqrt{64 - h^2}) = 8(ED)</cmath> | ||
| − | + | \\ | |
<math></math>(144 - h^2) - (64 - h^2) = 8(ED)<math> | <math></math>(144 - h^2) - (64 - h^2) = 8(ED)<math> | ||
| − | + | \\ | |
<cmath>80 = 8(ED)</cmath> | <cmath>80 = 8(ED)</cmath> | ||
| − | + | \\ | |
<cmath>ED = 10</cmath> | <cmath>ED = 10</cmath> | ||
| − | + | \\ | |
Adding up </math>AD<math> and </math>ED<math> we get </math>\fbox{E}$. | Adding up </math>AD<math> and </math>ED<math> we get </math>\fbox{E}$. | ||
Revision as of 10:00, 29 June 2024
Problem
In a circle with center 
, chord 
equals chord 
. Chord 
cuts 
in 
. If 
and 
, then 
equals:
Solution
Let 
be a point on 
so 
. Let 
, 
and 
. 
. Using Power of a Point on , 
(there isn't much information about the circle so I wanted to use PoP).
![\[(\sqrt{144 - h^2} - \sqrt{64 - h^2})(\sqrt{144 - h^2} + \sqrt{64 - h^2}) = 8(ED)\]](http://latex.artofproblemsolving.com/8/4/a/84a053195ec82b28f96649a3b2c28a9d2258d76a.png)
\\
$$ (Error compiling LaTeX. Unknown error_msg)(144 - h^2) - (64 - h^2) = 8(ED)
AD
ED
\fbox{E}$.
See Also
| 1958 AHSC (Problems • Answer Key • Resources) | ||
| Preceded by Problem 41 |
Followed by Problem 43 | |
| 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 | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
