All Questions ⁺⁰236075 Questions

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Geometry

Let $WXYZ$ be a trapezoid with bases $\overline{XY}$ and $\overline{WZ}$. In this trapezoid, $\angle ZXW = 120^\circ$, $\angle XWZ = 60^\circ$, and $\angle XYZ = 120^\circ$. Find $\angle YXZ$, in degrees.

crimefightingvigiI Dec 23, 2024

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+441

Geometry

In trapezoid $PQRS,$ $\overline{PQ} \parallel \overline{RS}$. Let $X$ be the intersection of diagonals $\overline{PR}$ and $\overline{QS}$. The area of triangle $PQX$ is $4,$ and the area of triangle $PSR$ is $8.$ Find the area of trapezoid read more ..

crimefightingvigiI Dec 23, 2024

Dec 22, 2024

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+781

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 $BE$.

booboo44 Dec 22, 2024

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+781

geometry

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.

booboo44 Dec 22, 2024

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+64

Halp with probability!

The grid below is made up of line segments, like the line segment in red.
[asy]
unitsize(1 cm);
int i;
for (i = 0; i <= 3; ++i) {
draw((i,0)--(i,2));<#> }<#> for (i = 0; i <= 2; ++i) {<#> draw((0,i)--(3,i));<#> read more ..

ghistory Dec 22, 2024

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+809

Geometry

In triangle ABC, \angle A = 90^\circ. Altitude $\overline{AP},$ angle bisector $\overline{AQ},$ and median $\overline{AR}$ are drawn. If $PQ = 3$ and $QC = 4,$ find $AR.$

gnistory Dec 22, 2024

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+809

Geometry

The centroid of triangle ABC is G. G_1, G_2, and G_3 are the centroids of triangles $BCG,$ $CAG,$ and $ABG,$ respectively. Find [ABC].

gnistory Dec 22, 2024

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+809

Geometry

The centroid of triangle ABC is G. Find BG.

gnistory Dec 22, 2024

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+809

Geometry

The centroid of triangle ABC is G. Find $x,$ in degrees.

gnistory Dec 22, 2024

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+395

Geometry

In triangle ABC, the orthocenter H lies on altitude $\overline{AD}.$ Find $\frac{AH}{HD}.$

MeIdHunter Dec 22, 2024

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+395

Geometry

Find the ratio of the area of the red region to the area of the yellow region. Enter your answer as a fraction.

MeIdHunter Dec 22, 2024

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+395

Geometry

Point H is the orthocenter of triangle ABC. If \angle BAC=118^\circ, what is \angle ABC in degrees?

MeIdHunter Dec 22, 2024

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+395

Geometry

The centroid of triangle ABC is G. Given $AD = 15$ and $CE = 20,$ find the area of triangle $ABC.$

MeIdHunter Dec 22, 2024

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+66

Geometry

The centroid of triangle ABC is G. Find AG.

cwimie Dec 22, 2024

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+66

Geometry

Triangle DEF is the medial triangle of triangle ABC, and triangle $XYZ$ is the medial triangle of triangle $DEF.$ If the area of triangle $XYZ$ is $8$, what is the area of triangle $ABC?$

cwimie Dec 22, 2024

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+66

Geometry

In triangle ABC, let M be the midpoint of \overline{AB} and N be on \overline{BC} such that $\overline{AN}$ is an altitude of triangle $ABC$. If $AN = MC = 13$ and $MN = 8$, and $\overline{AN}$ and $\overline{CM}$ intersect at $X$, then what is $ read more ..

cwimie Dec 22, 2024

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+66

Geometry

M is the midpoint of \overline{AB} and N is the midpoint of \overline{AC}, and $T$ is the intersection of $\overline{BN}$ and $\overline{CM}$, as shown. If $\overline{BN} \perp \overline{AC},$ $BM = 12$, and $BC = 18$, then find $CT$.

cwimie Dec 22, 2024

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+66

Geometry

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.

cwimie Dec 22, 2024

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+66

Geometry

Point D is the midpoint of median AM of triangle ABC. Point E is the midpoint of AB, and point T is the intersection of BD and ME. Find the area of triangle BEC if [ABC] = 14.

cwimie Dec 22, 2024

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+66

Geometry

Point $P$ is on side $\overline{AC}$ of triangle $ABC$ such that $\angle APB =\angle PBA$, and $\angle ABC - \angle ACB = 24^\circ$. Find $\angle PBC$ in degrees.

cwimie Dec 22, 2024

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+66

Geometry

A rectangle contains a strip of width $1,$ as shown below. Find the area of the strip.

cwimie Dec 22, 2024

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+66

Algebra

Let $m$ be a real number. If the quadratic equation $x^2+mx+4 = 2x^2 + 17x + 8$ has two distinct real roots, then what are the possible values of $m$? Express your answer in interval notation.

cwimie Dec 22, 2024

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+66

Algebra

Find the sum of the squares of the roots of $2x^2+4x-1=x^2-8x+3$.

cwimie Dec 22, 2024

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