2008 AMC 10B Problems/Problem 10
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Problem
Points
and
are on a circle of radius
and
. Point
is the midpoint of the minor arc
. What is the length of the line segment
?
Solution
Let the center of the circle be
, and let
be the intersection of
and
(then
is the midpoint of
).
, since they are both radii.
By the Pythagorean Theorem,
, and by subtraction,
.
Using the Pythagorean Theorem again,
.

See also
| 2008 AMC 10B (Problems • Resources) | ||
| Preceded by Problem 9 | Followed by Problem 11 | |
| 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 | ||





