February Regional Geometry Team: Question #1
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1 February Regional Geometry Team: Question #1 A = area of an equilateral triangle with a side length of 4. B = area of a square with a side length of 3. C = area of a regular hexagon with a side length of 4. C What is + B? A February Regional Geometry Team: Question #2 A is the number of sides a polygon has with 65 diagonals B is equal to 1 if part A is less than or equal to 10, or B is 2 if it is greater than 10 C is 20 if B is odd, or C is 25 if B is even B What is A + C
2 February Regional Geometry Team: Question #3 In a coordinate plane, a circle of radius 10 has its center at the origin. A square of side length 14 is externally tangent to the circle at the center of one of its sides. Let the shaded area be the area formed by the square circling the circle completely (meaning the square goes around the circle, still being tangent to the circle at the center of its side at all times). What is the area of this shaded area (anulus)? February Regional Geometry Team: Question #4 Four congruent circles are inscribed in a circle and each of the four are externally tangent to its two adjacent circles. Each of the four circles are also tangent to the larger circle at one point. The radius of the larger circle is 4. What is the radius of one of the smaller inscribed circles?
3 February Regional Geometry Team: Question #5 What is (A)(B)(C)? A = the radius of a circle that is circumscribed about a hexagon with an area of 12 3 B = the radius of a circle that is inscribed in an equilateral triangle with an area of 2 3 C = the length of a side of an octagon that is inscribed in a square of side length 4. The octagon has a maximum area. February Regional Geometry Team: Question #6 A cube has a length of 216. It is divided into 27 identical cubes. These cubes are each divided into 8 identical cubes. These new cubes are divided into 27 new identical cubes. These new cubes are divided into 8 more identical cubes. x y The sum of the surface areas of all of these cubes is equal to (2 )(3 ). What is (x)(y)?
4 February Regional Geometry Team: Question #7 Triangle ABC and DEF are similar. m B = m E = 90. If AB = 7, BC = 24, and DF = 50, what is the area of DEF? February Regional Geometry Team: Question #8 A boy wants to cut a square with the largest area out of a triangular card board paper with sides 5, 12, and 13. Find the length of a side of the square, given the corners of the square must be on the sides or corners of the triangle.
5 February Regional Geometry Team: Question #9 A pentagon ABCDE is inscribed in a circle. Arc AB = 80. What is m C + m E? February Regional Geometry Team: Question #10 Equilateral triangle ABC has length 4. A = length of the side of an equilateral triangle with 1/2 times the area of ABC B = length of the side of an equilateral triangle with 2 times the area of ABC C = length of the side of an equilateral triangle with 3 times the area of ABC D = length of the side of an equilateral triangle with 4 times the area of ABC What is AB + CD?
6 February Regional Geometry Team: Question #11 In an octagon, a diagonal is chosen at random. A = the probability that the diagonal chosen is neither the longest nor the shortest one. B = the probability that the diagonal chosen is the shortest one C = the probability that the diagonal chosen is the longest one What is (A)(B)(C)? February Regional Geometry Team: Question #12 There are two concentric circles. A chord of length 6 is drawn in the larger circle that is tangent to the smaller circle. The radius of the larger circle is 10 times bigger than the radius of the smaller circle. What is the area outside in the smaller circle but inside the larger circle?
7 February Regional Geometry Team: Question #13 Find the positive difference between the volume and surface area of a sphere with a radius of 4. February Regional Geometry Team: Question #14 A rhombus has diagonals of length 16 and 20. The diagonals are cut in half. What is the new area?
8 February Regional Geometry Team: Question #15 What is A + B + C? A = the number of sides in a polygon with 27 diagonals B = the number of sides in a polygon with 170 diagonals C = the number of sides in a regular polygon with angles of 144
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