All Questions ⁺⁰237293 Questions

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+782

Geometry

Semicircles are drawn on diameters \overline{AB} and \overline{CD}, as shown below. Find AB.

crimefightingvigiI Dec 27, 2024

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18

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+782

Geometry

The circle below centered at O has a radius of 5. Find CD.

crimefightingvigiI Dec 27, 2024

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18

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+782

Geometry

Two squares are inscribed in a semi-circle, as shown below. Find the radius of the semi-circle.
(See second diagram. Each square has side length 10.) read more ..

crimefightingvigiI Dec 27, 2024

0

13

1

+349

Geometry

A 3 \times 4 rectangle rolls along a line. The path taken by one of the corners is shown below. Find the length of the arc taken by the first step, where the radius is 3, and the angle of the arc is 90 degrees.

cwimie Dec 27, 2024

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13

1

+349

Geometry

Find the area of circular segment AB.

cwimie Dec 27, 2024

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18

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+349

Geometry

In triangle ABC, \overline{AD} is the angle bisector of \angle BAC, and $\angle B>\angle C.$ Which of the following inequalities must hold? Select all that apply.
AD + BC > AC + BD
BC + BD > AC + AD
AB + read more ..

cwimie Dec 27, 2024

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20

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+349

Geometry

In quadrilateral ABCD, the longest side is AB, and the shortest side is CD. Which of the following inequalities must hold? Select all that apply.
AB > BC
CD > AD
BC > AD read more ..

cwimie Dec 27, 2024

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15

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+1501

Geometry

Given a convex quadrilateral, let P be the perimeter, and let S be the sum of the diagonals. Which of the following inequalities always hold? Select all that apply.
P^2 > 4S
S + P > 10
S - P < 0 read more ..

learnmgcat Dec 27, 2024

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14

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+1501

Geometry

In triangle ABC, let D be a point on side \overline{BC}. Select all the true statements.
If $\overline{AD}$ is an altitude of triangle $ABC,$ then AB > BC.
If $\overline{AD}$ is a median of triangle $ABC,$ then AB >read more ..

learnmgcat Dec 27, 2024

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12

1

+1501

Geometry

All the sides of a triangle have integer length. The perimeter of the triangle is 8, and the triangle is isosceles. How many such non-congruent triangles are there?

learnmgcat Dec 27, 2024

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15

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+1501

Geometry

Point P lies on a circle centered at A with radius 3. Point $Q$ lies on a circle centered at $B$ with radius $2.$ If $AB = 4,$ then find the smallest possible length of $\overline{PQ}.$

learnmgcat Dec 27, 2024

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13

1

+1501

Geometry

What is the largest possible integer length of the third side of the triangle?
Two of the sides are 58 and 61.

learnmgcat Dec 27, 2024

Dec 26, 2024

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13

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+1501

Geometry

Point P lies in regular hexagon ABCDEF such that [ABP ] = 3, [CDP] = 3, and [EFP] = 3. Compute [BCP].

learnmgcat Dec 26, 2024

-2

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+1501

Geometry

Find the area of pentagon ABCDE.

learnmgcat Dec 26, 2024

-2

13

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+1501

Geometry

The diagram consists of two regular hexagons. Find the area of the red quadrilateral.

learnmgcat Dec 26, 2024

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8

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+1501

Geometry

Regular hexagon ABCDEF is inscribed in rectangle PQRS. If [AFP] = 20 and [ABC] = 25, then find [ABCDEF].

learnmgcat Dec 26, 2024

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20

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+1501

Geometry

Let A_1 A_2 A_3 \dotsb A_{12} be a regular polygon. If the area of A_1 A_2 A_3 \dotsb A_{12} is 1, then find the area of the blue region.

learnmgcat Dec 26, 2024

-2

21

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+1501

Geometry

Let ABCDEF be a regular hexagon. If the area of ABCDEF is 1, then find the area of the green region.

learnmgcat Dec 26, 2024

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21

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+1501

Geometry

Given a regular hexagon with side length 2, a square is constructed on each side of the hexagon. The whole figure is then enclosed inside a hexagon. Find the area of the hexagon.

learnmgcat Dec 26, 2024

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17

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+1556

Geometry

Let A_1 A_2 A_3 \dotsb A_{12} be a regular polygon. The center of the polygon is O. Find the area of the regular polygon.

kittykat Dec 26, 2024

-2

15

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+1556

Geometry

Regular octagon ABCDEFGH$ has an area of 1. Find the area of the yellow region.

kittykat Dec 26, 2024

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18

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+1556

Geometry

Points P, Q, R, S, and T lie on a circle of radius 2, as shown below. Find [PQRST].

kittykat Dec 26, 2024

-1

15

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+1556

Geometry

ABCDEFGH is a regular octagon. Find the ratio of the area of the red triangle to the area of the blue square.

kittykat Dec 26, 2024

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