2006 iTest Problems/Problem U2
Revision as of 00:19, 3 December 2018 by Rockmanex3 (talk | contribs) (Solution to Problem U2 -- Carved Quad in a Circle)
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) | ||
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 |