All Questions ⁺⁰236050 Questions

+1

45

0

+1911

hard counting problem

Find the number of ways of choosing three circles below, so that no two circles are next to each other.

tomtom Dec 22, 2023

+1

16

2

+1521

Polygon

Let P_1 P_2 P_3 \dotsb P_{10} be a regular polygon inscribed in a circle with radius $1.$ Compute
P_1 P_2 + P_2 P_3 + P_3 P_4 + \dots + P_9 P_{10} + P_{10} P_1

blackpanther Dec 22, 2023

-1

47

0

+1521

circles

In rectangle $EFGH$, let $M$ be the midpoint of $\overline{EF}$, and let $X$ be a point such that $MH = MX$, as shown below. If $\angle EFH = 30^\circ$ and $\angle MHX = 60^\circ,$ then find $\angle XHG,$ in degrees.

blackpanther Dec 22, 2023

-1

42

0

+1521

Circles

In the diagram, chords $\overline{XY}$ and $\overline{VW}$ are extended to meet at $U.$ If $\angle U = 30^\circ$, minor arc $XY$ is $180^\circ$, and minor arc $VW$ is $90^\circ$. Find arc $WY$, in degrees.

blackpanther Dec 22, 2023

-1

37

0

+1521

Semicircles

In triangle $ABC,$ $\angle B = 90^\circ.$ Semicircles are constructed on sides $\overline{AB},$ $\overline{AC},$ and $\overline{BC},$ as shown below. Find the area of the shaded region.

blackpanther Dec 22, 2023

0

46

1

+1521

Area

The rectangle below has been divided into unit squares. Find the total area of the blue shaded region, in square units.
read more ..

blackpanther Dec 22, 2023

0

29

0

+1521

triangle

Point $P$ is on side $\overline{AC}$ of triangle $ABC$ such that $\angle APB =\angle ABP$, and $\angle ABC - \angle BAC = 42^\circ$. Find $\angle PBC$ in degrees.

blackpanther Dec 22, 2023

-1

44

0

+1521

Circle

In the diagram below, chords $\overline{AB}$ and $\overline{CD}$ are perpendicular, and meet at $X.$ Find the diameter of the circle.

blackpanther Dec 22, 2023

-1

28

1

+1521

Circle

A sector of a circle is shown below. The sector has an area of $60 \pi.$ What is the radius of the circle?

blackpanther Dec 22, 2023

0

18

1

+4

Inequalities

Let be real numbers such that
What is the largest possible value of

ndoxxx Dec 22, 2023

0

30

1

+1455

coordinates

What is the area of the region bounded by the graphs of $y = |x + 2| - |x - 2|$ and $y = |x + 1| - |x - 5|$?

kittykat Dec 22, 2023

0

35

1

+1455

Minimum

What is the minimum possible perimeter of a triangle two of whose sides are along the $x$- and $y$-axes and such that the third contains the point $(1,1)$?

kittykat Dec 22, 2023

0

31

1

+1455

Coordinates

Find the minimum distance from any lattice point to the line $y = \frac{5}{3} x + \frac{12}{7}.$

kittykat Dec 22, 2023

0

21

2

+1678

square and triangles

The diagram below consists of a small square, four equilateral triangles, and a large square. Find the area of the large square.

wiseowl Dec 22, 2023

0

27

0

+1678

cyclic quadrilateral

In cyclic quadrilateral $PQRS,$
angle P = angle Q = angle R
Find the largest angle in quadrilateral $PQRS,$ in degrees.

wiseowl Dec 22, 2023

0

39

0

+1678

Circles

Trapezoid $HGFE$ is inscribed in a circle, with $\overline{EF} \parallel \overline{GH}$. If arc $GH$ is $66$ degrees, arc $EH$ is $x^2 + 8x$ degrees, and arc $FG$ is $25 + 16x$ degrees, where $x > 0,$ find arc $EPF$, in degrees.

wiseowl Dec 22, 2023

0

23

0

+1678

circles

In the diagram below, $O$ is the center of the circle, and $\overline{UV}$ is a diameter. Find $\angle XYZ$, in degrees.

wiseowl Dec 22, 2023

0

29

1

+1678

circle angles

Points $L$ and $M$ lie on a circle $\omega_1$ centered at $O$. The circle $\omega_2$ passing through points $O,$ $L,$ and $M$ is drawn. If the measure of arc $LM$ in circle $\omega_1$ is $90^\circ,$ and the radius of $\omega_1$ is 1, then find read more ..

wiseowl Dec 22, 2023

0

47

0

+1678

Geometry

In the figure, if the measure of arc $FG$ is $118^\circ$, the measure of arc $FQ$ is $25^\circ$, and $FR = FQ,$ then what is $\angle RPG$, in degrees?

wiseowl Dec 22, 2023

0

36

1

+1768

Trapezoid

Trapezoid $ABCD$ is inscribed in the semicircle with diameter $\overline{AB}$, as shown below. Find the radius of the semicircle. Find the area of ABCD.
PQDC is a square. read more ..

bader Dec 22, 2023

0

39

0

+1911

Triangle

Triangle ABC has sides AB = 7, BC = 8, and AC = 9. Point C is reflected over line AB to create point C'. Next, point B is reflected over line AC' to create point B'. Find the area of triangle B'C'C.

tomtom Dec 22, 2023

0

40

1

+101

Geometry problem

A conical frustum has bases with radii of 9 and 12, and a height of 4 The total surface area of the frustum is A, in square units, and the volume of the frustum is V, in cubic units. Find A+V

Vxritate Dec 22, 2023

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