Difference between revisions of "1958 AHSME Problems/Problem 42"
Pateywatey (talk | contribs) (→Solution) |
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> | ||
\\ | \\ | ||
− | < | + | <cmath>(144 - h^2) - (64 - h^2) = 8(ED)</cmath> |
\\ | \\ | ||
<cmath>80 = 8(ED)</cmath> | <cmath>80 = 8(ED)</cmath> | ||
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<cmath>ED = 10</cmath> | <cmath>ED = 10</cmath> | ||
\\ | \\ | ||
− | Adding up < | + | Adding up <math>AD</math> and <math>ED</math> we get <math>\fbox{E}</math>. |
== See Also == | == See Also == |
Revision as of 11:01, 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).
\\
\\
\\
\\
Adding up
and
we get
.
See Also
1958 AHSC (Problems • Answer Key • Resources) | ||
Preceded by Problem 41 |
Followed by Problem 43 | |
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All AHSME Problems and Solutions |
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