Download Hagerty Invitational Geometry Team: Question #1 Let

Hagerty Invitational
Geometry Team: Question #1
Let be the area of a circle with radius .
Let be the perimeter of a circle with radius .
Let be the length of the longest chord that can be drawn in a circle with radius
.
Let be the area of a semicircle with radius
.
Find
.
Hagerty Invitational
Geometry Team: Question #1
Let be the area of a circle with radius .
Let be the perimeter of a circle with radius .
Let be the length of the longest chord that can be drawn in a circle with radius
.
Let be the area of a semicircle with radius
.
Find
.
Hagerty Invitational
Geometry Team: Question #2
For the following questions, refer to a regular hexagon with sides of length 4.
Let be the length of the longest diagonal in the hexagon.
Let be the maximum number of diagonals that can be drawn in the hexagon.
Let be perpendicular distance between two opposite sides.
Let be the area of the hexagon.
Find
.
Hagerty Invitational
Geometry Team: Question #2
For the following questions, refer to a regular hexagon with sides of length 4.
Let be the length of the longest diagonal in the hexagon.
Let be the maximum number of diagonals that can be drawn in the hexagon.
Let be perpendicular distance between two opposite sides.
Let be the area of the hexagon.
Find
.
Hagerty Invitational
Geometry Team: Question #3
Find the sum of the first 8 terms in the geometric sequence with first term 2 and common ratio 3.
Hagerty Invitational
Geometry Team: Question #3
Find the sum of the first 8 terms in the geometric sequence with first term 2 and common ratio 3.
Hagerty Invitational
In star GEOISBALRZ to the right,
Let
Let
Let
Let
Let
Let
Find
be the measure in degrees of
.
be the measure in degrees of EIB.
be the measure in degrees of
be the measure in degrees of
be the measure in degrees of
.
be the measure in degrees of
.
Hagerty Invitational
In star GEOISBALRZ to the right,
Let
Let
Let
Let
Let
Let
Find
be the measure in degrees of
.
be the measure in degrees of EIB.
be the measure in degrees of
be the measure in degrees of
be the measure in degrees of
.
be the measure in degrees of
.
Geometry Team: Question #4
Z
Geometry Team: Question #4
Z
Hagerty Invitational
How many diagonals does a convex 2011-gon have?
Geometry Team: Question #5
Hagerty Invitational
How many diagonals does a convex 2011-gon have?
Geometry Team: Question #5
Hagerty Invitational
In the diagram with angles of measure
and ,
, find
Geometry Team: Question #6
.
, find
Geometry Team: Question #6
.
_
+
Hagerty Invitational
In the diagram with angles of measure
_
+
and ,
Hagerty Invitational
In the diagram to the right,
Let be the ratio of lengths
Let be the ratio of areas of
Geometry Team: Question #7
to
.
to
.
Express the ratios as a fraction. Find .
Hagerty Invitational
In the diagram to the right,
Let be the ratio of lengths
Let be the ratio of areas of
Geometry Team: Question #7
to
.
to
Express the ratios as a fraction. Find .
.
Hagerty Invitational
How many of the following statements are true?





All pairs of lines that do not intersect are parallel.
The geometric mean of and is
The diagonal of a cube with edges of length is
If the cosine of angle is
, the sine of is
.
A cube can be inscribed in a sphere.
Hagerty Invitational
How many of the following statements are true?





Geometry Team: Question #8
All pairs of lines that do not intersect are parallel.
The geometric mean of and is
The diagonal of a cube with edges of length is
If the cosine of angle is
, the sine of is
.
A cube can be inscribed in a sphere.
Geometry Team: Question #8
Hagerty Invitational
Geometry Team: Question #9
Use the following coordinates for this question: A (-5, 3); W (-2, 9); E (4, 8); S (7, 1); U (2, -3);
M (-3, -3).
Let be the area of the quadrilateral AWEM.
Let be the area of the quadrilateral SUME.
What is
Hagerty Invitational
Geometry Team: Question #9
Use the following coordinates for this question: A (-5, 3); W (-2, 9); E (4, 8); S (7, 1); U (2, -3);
M (-3, -3).
Let be the area of the quadrilateral AWEM.
Let be the area of the quadrilateral SUME.
What is
Hagerty Invitational
Geometry Team: Question #10
In a 9-12-15 right triangle, what is the sum of the altitudes drawn to each side of the triangle?
Hagerty Invitational
Geometry Team: Question #10
In a 9-12-15 right triangle, what is the sum of the altitudes drawn to each side of the triangle?
Hagerty Invitational
In rectangle
,
and
.
What is the area of quadrilateral
Hagerty Invitational
In rectangle
,
and
.
What is the area of quadrilateral
Geometry Team: Question #11
,
,
?
Geometry Team: Question #11
,
?
,
Hagerty Invitational
Geometry Team: Question #12
Let be the angle in degrees of , if the complement of is one third of the supplement of .
Let be the angle in degrees of , if three times is equal to two times the supplement of .
Find .
Hagerty Invitational
Geometry Team: Question #12
Let be the angle in degrees of , if the complement of is one third of the supplement of .
Let be the angle in degrees of , if three times is equal to two times the supplement of .
Find .
Hagerty Invitational
Geometry Team: Question #13
How many distinct permutations of the word MISTRESSSHIP are there?
Hagerty Invitational
Geometry Team: Question #13
How many distinct permutations of the word MISTRESSSHIP are there?
Hagerty Invitational
Geometry Team: Question #14
What is the measure in degrees of one exterior angle of a regular 2011-gon?
Hagerty Invitational
Geometry Team: Question #14
What is the measure in degrees of one exterior angle of a regular 2011-gon?
Hagerty Invitational
Geometry Team: Question #15
Let A be the area of an equilateral triangle with sides of length 3.
Let B be the hypotenuse of a triangle with legs of length 9 and 40.
Let C be the volume of a cylinder with radius 3 and height 3.
Find
Hagerty Invitational
Geometry Team: Question #15
Let A be the area of an equilateral triangle with sides of length 3.
Let B be the hypotenuse of a triangle with legs of length 9 and 40.
Let C be the volume of a cylinder with radius 3 and height 3.
Find