All Questions ⁺⁰237753 Questions

Jan 16, 2025

0

36

1

+987

Geometry

In the diagram below, SR = PQ = 20 and RT:TS = 2:5. Find UV.

booboo44 Jan 16, 2025

+1

19

1

+987

Geometry

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 ..

booboo44 Jan 16, 2025

0

40

0

+987

Geometry

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.

booboo44 Jan 16, 2025

0

42

0

+987

Geometry

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

booboo44 Jan 16, 2025

0

27

2

+1761

Geometry

In a certain regular polygon, the measure of each interior angle is $2$ times the measure of each exterior angle. Find the number of sides in this regular polygon.

parmen Jan 16, 2025

0

41

1

+1761

Geometry

In triangle $ABC,$ $\angle B = 90^\circ.$ Point $X$ is on $\overline{AC}$ such that $\angle BXA = 90^\circ,$ $AX = 5,$ and $CX = 5$. What is $BX$?

parmen Jan 16, 2025

0

38

1

+1761

Geometry

In triangle $ABC$, $AB = 10$ and $AC = 15$. Let $D$ be the foot of the perpendicular from $A$ to $BC$. If $BD:CD = 1:3$, then find $AD$.

parmen Jan 16, 2025

0

45

1

+1761

Geometry

We have a triangle $\triangle ABC$ and a point $K$ on $BC$ such that $AK$ is an altitude to $\triangle ABC$. If $AC = 8,$ $BK = 2$, and $CK = 3,$ then what is $AB$?

parmen Jan 16, 2025

0

44

0

+1808

Geometry

Let $k$ be a positive real number. The line $x + y = 3 + k$ and the circle $x^2 + y^2 = k$ are drawn. Find $k$ so that the line is tangent to the circle.

blackpanther Jan 16, 2025

0

28

1

+1808

Geometry

In right triangle $ABC,$ $\angle C = 90^\circ$. Median $\overline{AM}$ has a length of 2, and median $\overline{BN}$ has a length of 3. What is the length of the hypotenuse of the triangle?

blackpanther Jan 16, 2025

0

31

1

+1808

Geometry

Two tangents $\overline{PA}$ and $\overline{PB}$ are drawn to a circle, where $P$ lies outside the circle, and $A$ and $B$ lie on the circle. The length of $\overline{PA}$ is $3,$ and $AB$ has a length of 8. Find the radius of the circle.</ read more ..

blackpanther Jan 16, 2025

0

33

1

+1808

Geometry

A circular table is pushed into a corner of the room, where two walls meet at a right angle. A point $P$ on the edge of the table (as shown below) has a distance of $1$ from one wall, and a distance of $2$ from the other wall. Find the radius read more ..

blackpanther Jan 16, 2025

+3

24

1

+38

geometry problem help

The two bases of a cylinder are two parallel cross sections of a sphere. We know the radius of the sphere is 3 and the height of the cylinder is 4 Find the volume of the cylinder.
[asy] size(4cm); import three; currentprojection=orthographic(0,2,0.2);read more ..

skibidibrain901 Jan 16, 2025

Jan 15, 2025

0

46

0

+1524

Geometry

In triangle $ABC,$ $\angle C = 90^\circ.$ A semicircle is constructed along side $\overline{AC}$ that is tangent to $\overline{BC}$ and $\overline{AB}.$ If the radius of the semicircle is equal to $1$ and $AB = 2$, then find $AC.$

learnmgcat Jan 15, 2025

0

46

0

+1524

Geometry

The tangent to the circumcircle of triangle $WXY$ at $X$ is drawn, and the line through $W$ that is parallel to this tangent intersects $\overline{XY}$ at $Z.$ If $XZ = 5$ and $YZ = 2,$ find $WX.$

learnmgcat Jan 15, 2025

+1

39

1

+608

Algebra

One ordered pair $(a,b)$ satisfies the two equations $ab^4 = 48$ and $ab^3 = 24$. What is the value of b in this ordered pair?

onyuIee Jan 15, 2025

0

38

1

+608

Algebra

Let $a$ and $b$ be complex numbers. If $a + b = 1$ and $a^2 + b^2 = 2,$ then what is $a^3 + b^3?$

onyuIee Jan 15, 2025

0

24

1

+608

Algebra

Let $a_1,$ $a_2,$ $a_3,$ $\dots$ be a sequence. If
\[a_n = a_{n - 1} + a_{n - 2}\]
for all $n \ge 3,$ and $a_{11} = 1$ and $a_{10} = 4,$ then find $a_6.$

onyuIee Jan 15, 2025

0

30

1

+2730

Geometry

Find the coordinates of the center of the circle.

LiIIiam0216 Jan 15, 2025

0

39

1

+2730

Geometry

Rose has a spherical plum of radius $2$ and a spherical watermelon of radius $8$. She builds a glass sphere around the two fruits to contain them, making the sphere as small as possible. When she has done this, she places a golf ball inside read more ..

LiIIiam0216 Jan 15, 2025

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