1985 AHSME Problems/Problem 22
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Problem
In a circle with center ,
is a diameter,
is a chord,
and
. Then the length of
is
Solution
Since is an angle inscribed in a
arc, we obtain
, so
is a
-
-
right triangle. This gives
and
, and now since
is a diameter,
. The fact that
is a diameter also means that
, so
is again a
-
-
right triangle, yielding
and
, which finally gives
.
See Also
1985 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 21 |
Followed by Problem 23 | |
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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