Difference between revisions of "1974 AHSME Problems/Problem 5"
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[[Category:Introductory Geometry Problems]] | [[Category:Introductory Geometry Problems]] | ||
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Latest revision as of 12:42, 5 July 2013
Problem
Given a quadrilateral inscribed in a circle with side
extended beyond
to point
, if
and
, find
.
Solution
Since is cyclic, opposite angles must sum to
. Therefore,
, and
. Notice also that
and
form a linear pair, and so they sum to
. Therefore,
. Notice that the answer didn't even depend on
.
See Also
1974 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 4 |
Followed by Problem 6 | |
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 |
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