crimefightingvigiI

93 Questions
4 Answers

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Geometry

A line and a circle intersect at $A$ and $B,$ as shown below. Find the distance between $A$ and $B$.
The circle is x^2 + y^2 = 1, and the line is y = x.

crimefightingvigiI Dec 10, 2024

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Geometry

Chords UV, WX, and YZ of a circle are parallel. The distance between chords UV and WX is 1, and the distance between chords WX and YZ is also 1. If UV =6 and YZ = 4, then find WX.

crimefightingvigiI Dec 10, 2024

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+382

Geometry

In triangle $PQR,$ $M$ is the midpoint of $\overline{QR}.$ Find $PM.$
PQ = 5, PR = 8, QR = 11

crimefightingvigiI Dec 8, 2024

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+382

Geometry

There are four cities: Capital City, Little Village, Mytown, and Yourtown. The distance from Capital City to Little Village is $5$ miles. The distance from Capital City to Mytown is $2$ miles. The distance from Mytown to Yourtown is $3$ read more ..

crimefightingvigiI Dec 8, 2024

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Geometry

Triangle ABC has altitudes AD, BE, and CF. If AD=12, BE=16, and CF is a positive integer, then find the largest possible value of CF

crimefightingvigiI Dec 7, 2024

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Geometry

The area of a trapezoid is $80$. The length of one base is $16$ units greater than the other base, and one base of the trapezoid is $12$. Find the length of the median of the trapezoid.

crimefightingvigiI Dec 7, 2024

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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 7, 2024

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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 $2,$ and the area of triangle $RSX$ is $2.$ Find the area of trapezoid read more ..

crimefightingvigiI Dec 7, 2024

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+382

Algebra

Let
f(x) = \sqrt{x - \sqrt{x}}.
Find the largest three-digit value of $x$ such that $f(x)$ is an integer.

crimefightingvigiI Dec 6, 2024

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+382

Algebra

Evaluate $a^3 - \dfrac{1}{a^3}$ if $a - \dfrac{1}{a} = 0$.

crimefightingvigiI Dec 6, 2024

+382

-1

The area of trapezoid PQRS is 18.

crimefightingvigiIDec 11, 2024

+382

-1

Angle YXZ is 45 degrees.

crimefightingvigiIDec 11, 2024

+382

-1

The answer is b/(2a).

crimefightingvigiIDec 11, 2024

+382

-1

The area of the strip is 120/7.

crimefightingvigiIDec 10, 2024