Amc 10 a amc 12 a problem 09 apply the pythagorean

2008 AMC 10 A, Problem #14 —
2008 AMC 12 A, Problem #09 —
“Apply the Pythagorean Theorem to find out height and width of the
screen.”
Difficulty: Medium-hard
NCTM Standard: Geometry Standard: use trigonometric relationships to determine lengths and
angle measures.
Mathworld.com Classification: Geometry > Plane Geometry > Triangles > Triangle Properties
> Pythagorean Theorem

Yesterday Han drove 1 hour longer than Ian at an average speed 5 miles
per hour faster than Ian. Jan drove 2 hours longer than Ian at an average
speed 10 miles per hour faster than Ian. Han drove 70 miles more than
Ian. How many more miles did Jan drive than Ian?
2008 AMC 10 A, Problem #15 —
“Set up equation to represent the relations with Ian’s total time, h hours,
and average speed, r miles.”
Difficulty: Medium-hard
NCTM Standard: Algebra Standard: use symbolic algebra to represent and explain mathematical
relationships.
Mathworld.com Classification: None

Points A and B lie on a circle centered at O , and
∠ AOB = 60
◦
. A second circle is internally tangent
to the first and tangent to both OA and OB . What
is the ratio of the area of the smaller circle to that of
the larger circle?
(A)
1
16
(B)
1
9
(C)
1
8
(D)
1
6
(E)
1
4