All Questions ⁺⁰235720 Questions

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Pyramid

Let $ABCDE$ be a right square pyramid, with base $ABCD$ and apex $E.$ Find the volume of the pyramid.

bader Dec 31, 2023

+1

51

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+1911

circle

A circle is centered at $O.$ The tangent to the circle at $P$ is extended to $Q.$ Line segment $\overline{QS}$ intersects the circle at $R.$ Find the area of the circle.

tomtom Dec 31, 2023

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49

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+1911

circles

Let $\overline{TU}$ and $\overline{VW}$ be chords of a circle, which intersect at $S$, as shown. Find $SW$.

tomtom Dec 31, 2023

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45

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+1911

chords

Chords $\overline{AB}$ and $\overline{CD}$ of a circle meet at $P$. If $AP = 3 \cdot PB$, then what is $AB$?

tomtom Dec 31, 2023

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43

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+1911

tangent

Let $X$, $Y$, and $Z$ be points on a circle. Let line $XY$ and the tangent to the circle at $Z$ intersect at $W$. If $\overline{WY} \perp \overline{WZ}$, then find $YZ$.

tomtom Dec 31, 2023

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52

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+1911

chords

Chords $\overline{AB}$ and $\overline{CD}$ of a circle meet at $P$. If $AP = 3 \cdot PB$, then what is $AB$?

tomtom Dec 31, 2023

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48

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+1911

chords

Chords $\overline{PR}$ and $\overline{QS}$ of a circle are perpendicular. Find $RS$.

tomtom Dec 31, 2023

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52

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+1911

circle

Let $\overline{AB}$ and $\overline{CD}$ be chords of a circle, that meet at point $Q$ inside the circle. If $CD = 34$, then find the minimum length of $CQ$.

tomtom Dec 31, 2023

-1

49

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+1443

rectangle

Rectangle $ABCD$ contains a point $X$ such that $AX = 3$, $BX = 3$, and $CX = 5$. Find $DX$.

blackpanther Dec 31, 2023

-1

11

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+1443

rhombus

In a rhombus, all the side lengths are $12,$ and one of the angles is equal to $150^\circ.$ Find the area of the rhombus.

blackpanther Dec 31, 2023

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55

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+1443

quadrilateral

In quadrilateral $PQRS$, $PQ = QR = RS = SP$, $PR = 8$, and $QS = 8$. Find the perimeter of $PQRS$.

blackpanther Dec 31, 2023

-1

16

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+1443

polynomial

There exists a polynomial f(x) and a constant k such that
(x^2 - 2x - 5) f(x) = 2x^4 - 4x^3 + kx^2.
What is k?

blackpanther Dec 31, 2023

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51

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+1439

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 $A = (0,0),$ $B = (1,0),$ and $C = (-1,0)$, then find the constant read more ..

kittykat Dec 31, 2023

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45

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+1439

coordinates

Let $O$ be the origin. Points $P$ and $Q$ lie in the first quadrant. The slope of line segment $\overline{OP}$ is $8,$ and the slope of line segment $\overline{OQ}$ is $11.$ If $OP = OQ,$ then compute the slope of line segment $\overline{PQ}.$
Note: read more ..

kittykat Dec 31, 2023

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21

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+1439

coordinates

A line and a circle intersect at $A$ and $B,$ as shown below. Find the coordinates of the midpoint of $\overline{AB}$.
The circle is x^2 + y^2 = 6. The line is x + y = 2.

kittykat Dec 31, 2023

-1

41

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+1443

Geometry

Can anyone give a hint here?
In square ABCD, point M is the midpoint of CD. Find the ratios of the areas of the four reigons that are formed. read more ..

blackpanther Dec 31, 2023

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