All Questions ⁺⁰235721 Questions

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Pyramid

A right pyramid has a square base. The area of each triangular face is one-third the area of the square face. If the total surface area of the pyramid is $432$ square units, then what is the volume of the pyramid in cubic units? read more ..

blackpanther Feb 26, 2024

-1

1

0

+1443

Bisector

In triangle $ABC$, $\angle ABC = 90^\circ$, and $D$ is on side $\overline{BC}$ such that $\overline{AD}$ bisects $\angle BAC$. If $AB = 4,$ $BC = 3$, and $AC = 5,$ then find the area of $\triangle ADC$. Round your answer to the nearest integer.</ read more ..

blackpanther Feb 26, 2024

-1

42

1

+1768

Coordinates

A line and a circle intersect at A and B, as shown below. Find the coordinates of the midpoint of AB.
The circle is x^2 + y^2 = 1, and the line is x + y = sqrt(2).

bader Feb 26, 2024

-1

23

1

+1768

Coordinates

A circle passes through the point $A,$ and is tangent to the $y$-axis at the point $B,$ as shown. Find the radius of the circle.
In the diagram, A = (1,0) and B = (0,1).

bader Feb 26, 2024

0

17

1

+1768

help with coordinates

A rectangle in the coordinate plane is shown below. A line with slope $\frac{1}{3}$ splits this rectangle into two regions with equal area. What is the $y$-intercept of this line?
The rectangle has coordinates (-1,-1), (-1,1), (1,1), read more ..

bader Feb 26, 2024

-1

1

1

+1911

Angle Bisector

In the diagram, $\overline{CX}$ bisects $\angle ACB$. Find the ratio of the area of triangle $BCX$ to the area of triangle $ACX$. Express your answer as a common fraction. read more ..

tomtom Feb 26, 2024

-2

31

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+1911

help geometry

In triangle $ABC$, let the perpendicular bisector of $BC$ intersect $BC$ and $AC$ at $D$ and $E$, respectively. If $BC = 20$ and $\angle C = 15^\circ$, then find the length of $BE$.

tomtom Feb 26, 2024

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24

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+1911

Triangle question

In triangle $ABC$, let $I$ be the incenter of triangle $ABC$. The line through $I$ parallel to $BC$ intersects $AB$ and $AC$ at $M$ and $N$, respectively. If $AB = 5$, $AC = 5$, and $BC = 8$, then find the area of triangle $AMN$.

tomtom Feb 26, 2024

-1

36

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+50

Can't figure out complex plane problem

Looking at the complex plane below, let let be the set of all complex numbers satisfying |w+z| = |w| + |z| for the complex number . Which of the complex numbers on the graph (s, t, u, v, w) are in set ? read more ..

helloworldhello Feb 26, 2024

Feb 25, 2024

-1

38

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+1678

Triangle

In triangle $ABC$, let $I$ be the incenter of triangle $ABC$. The line through $I$ parallel to $BC$ intersects $AB$ and $AC$ at $M$ and $N$, respectively. If $AB = 5$, $AC = 5$, and $BC = 8$, then find the area of triangle $AMN$.

wiseowl Feb 25, 2024

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33

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+1678

Coordinates

Points $A$, $B$, and $C$ are on a circle such that $AB = 8$, $BC = 15$, and $AC = 12$. Find the radius of the circle.

wiseowl Feb 25, 2024

-1

18

0

+1678

Geometry

In triangle $ABC$, $M$ is the midpoint of $\overline{BC}$, and $N$ is the midpoint of $\overline{AC}$. The perpendicular bisectors of $BC$ and $AC$ intersect at a point $O$ inside the triangle. If $\angle AOB = 90^\circ$, then find the measure read more ..

wiseowl Feb 25, 2024

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18

3

+0

I need help with substitution

isasejahr Feb 25, 2024

-1

35

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+1533

Coordinates

Points $A,$ $B,$ and $C$ are given in the coordinate plane. There exists a point $Q$ and a constant $k$ such that for any point $P$,
\[PA^2 + PB^2 + PC^2 = 3PQ^2 + k.\]
If $A = (7,-11),$ $B = (10,13),$ and $C = (18,-22)$, then find the constant read more ..

parmen Feb 25, 2024

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33

1

+1533

Coordinates

The line $y = mx$ bisects the angle between the two lines shown below. Find $m$.

parmen Feb 25, 2024

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30

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+1533

Circle

Let $x$ and $y$ be real numbers. If $x$ and $y$ satisfy
\[x^2 + y^2 = 4x - 8y + 17x - 5y + 25,\]
then find the largest possible value of $x.$ Give your answer in exact form using radicals, simplified as far as possible.

parmen Feb 25, 2024

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