Difference between revisions of "1974 AHSME Problems/Problem 5"
(Created page with "==Problem== Given a quadrilateral <math> ABCD </math> inscribed in a circle with side <math> AB </math> extended beyond <math> B </math> to point <math> E </math>, if <math> \mea...") |
m (added category) |
||
Line 9: | Line 9: | ||
==See Also== | ==See Also== | ||
{{AHSME box|year=1974|num-b=4|num-a=6}} | {{AHSME box|year=1974|num-b=4|num-a=6}} | ||
+ | [[Category:Introductory Geometry Problems]] |
Revision as of 10:17, 30 May 2012
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 |