2006 iTest Problems/Problem U2
The following problem is from the Ultimate Question of the 2006 iTest, where solving this problem required the answer of a previous problem. When the problem is rewritten, the T-value is substituted.
Problem
Points and
lie on a circle centered at
such that
is right. Points
and
lie on radii
and
respectively such that
,
, and
. Determine the area of quadrilateral
.
Solution
Let be the length of
. The radius of the circle is
, so the length of
is
. By the Pythagorean Theorem,
Since lengths must be positive,
. The area of
equals the area of
minus the area of
, so
.
See Also
2006 iTest (Problems, Answer Key) | ||
Preceded by: Problem U1 |
Followed by: Problem U2 | |
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 • 31 • 32 • 33 • 34 • 35 • 36 • 37 • 38 • 39 • 40 • U1 • U2 • U3 • U4 • U5 • U6 • U7 • U8 • U9 • U10 |