B
C
d
d
Difficulty:
Hard
NCTM Standard:
Geometry Standard for Grade 9-12: explore relationships (including congruence
and similarity) among classes of two- and three-dimensional geometric objects, make and test
conjectures about them, and solve problems involving them.
Mathworld.com Classification:
Geometry
>
Plane Geometry
>
Miscellaneous Plane Geometry
>
Area

A circle passes through the three vertices of anisosceles triangle that has two sides of length 3 and abase of length 2. What is the area of this circle?
(A)2π(B)52π(C)8132π(D)3π(E)72π
2007 AMC 10 B, Problem #11—“DrawBDto be an altitude of the isosceles4ABC.”
8

Difficulty:
Hard
NCTM Standard:
Geometry Standard for Grade 9-12: Analyze characteristics and properties oftwo- and three-dimensional geometric shapes and develop mathematical arguments about geometricrelationships .
Mathworld.com Classification:
Geometry
>
Plane Geometry
>
Triangles
>
Special Triangles
>
Other Triangles
>
Isosceles Triangle
Geometry
>
Plane Geometry
>
Circles

Tom’s age isTyears, which is also the sum of theages of his three children. His ageNyears ago wastwice the sum of their ages then. What isT/N?
2007 AMC 10 B, Problem #12—“The sum of his three children’s agesNyears ago wasT-3N.”
Difficulty:
Hard
NCTM Standard:
Number and Operations Standard for Grade 9-12: Understand numbers, ways
of representing numbers, relationships among numbers, and number systems.
Mathworld.com Classification:
Number Theory
>
Arithmetic
>
Addition and Subtraction
Number Theory
>
Arithmetic
>
Fractions
>
Proportional

Two circles of radius 2 are centered at(2,0)and at(0,2).What is the area of the intersection of theinteriors of the two circles?
(A)π-2(B)π2(C)π3(D)2(π-2)(E)π
√
3