All Questions ⁺⁰234659 Questions

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Incenter

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 $AMN$.

Vxrtate Feb 12, 2024

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30

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Triangles

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 $BE$.

Vxrtate Feb 12, 2024

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24

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Geometry

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 ..

Vxrtate Feb 12, 2024

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3

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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 ..

Vxrtate Feb 12, 2024

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31

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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 ..

Vxrtate Feb 12, 2024

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24

1

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Geometry

In triangle ABC, the angle bisector of angle BAC meets BC at D. If angle BAC=60 degrees, angle ABC=60 degrees and AD=24 then find the area of triangle ABC.

Vxrtate Feb 12, 2024

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3

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Area

Find the area of triangle ABC if AB=6, BC=8 and angle ABC=35 degrees

Vxrtate Feb 12, 2024

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24

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Triangle

In triangle $ABC$, $\angle A = 30^\circ$ and $\angle B = 90^\circ$. Point $X$ is on side $\overline{AC}$ such that line segment $\overline{BX}$ bisects $\angle ABC$. If $BC = 12$, then find the area of triangle $BXA$.

Vxrtate Feb 12, 2024

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4

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Square in Triangle

A square is inscribed in a right triangle, as shown below. The legs of the triangle are 1 and 3. Find the area of the square.

Vxrtate Feb 12, 2024

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17

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+101

Geometry Problem

Find the area of triangle ABC.

Vxritate Feb 12, 2024

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20

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+39

Help, and please explain

The two circles below are externally tangent. A common external tangent intersects line at Find line PQ at R. Find QR.

There are two circles touching, circle 1 has a point in the middle that extends to the border read more ..

rerebas Feb 12, 2024

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22

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+101

Geometry Problem

Triangle DEF is equilateral. Find AE.

hairyberry ●●

Vxritate Feb 12, 2024

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Square

In square ABCD, P is on BC such that BP = 4 and PC = 1, and Q is on line CD such that DQ = 2 and QC = 3. Find sin angle PAQ.

Vxrtate Feb 12, 2024

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33

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help with triangles

In triangle PQR, M is the midpoint of PQ. Let X be the point on QR such that PX bisects angle QPR, and let the perpendicular bisector of PQ intersect AX at Y. If PQ = 36, PR = 22, QR = 26, and MY = 8, then find the area of triangle PQR

Vxrtate Feb 12, 2024

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18

5

+101

Geometry Problem

Semicircles are constructed on AB, AC, and BC. A circle is tangent to all three semicircles. Find the radius of the circle.

proyaop ●●●●●

Vxritate Feb 12, 2024

Feb 11, 2024

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Algebra

1) Write a simplified equation for the set of points that are equally far from (12, 0) as they are from (3, 0).
2) Write a simplified equation for the set of points that are exactly twice as far from (12, 0) as they are from read more ..

Lilliam0216 Feb 11, 2024

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22

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Tricky Triangle

In triangle $ABC,$ $AC = BC$ and $\angle ACB = 90^\circ.$ Points $P$ and $Q$ are on $\overline{AB}$ such that $P$ is between $A$ and $Q$ and $\angle QCP = 45^\circ.$ If cos ACP = 2/3, then find cos BCQ.

Vxrtate Feb 11, 2024

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32

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Cube in Pyramid

In tetrahedron ABCO, angle AOB = angle AOC = angle BOC = 90^\circ. A cube is inscribed in the tetrahedron so that one of its vertices is at O, and the opposite vertex lies on face ABC. Let OA = 1, OB = 1, OC = 1. Find the volume of read more ..

Vxrtate Feb 11, 2024

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21

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Right triangle

In triangle $ABC,$ $\angle B = 90^\circ.$ Semicircles are constructed on sides $\overline{AB},$ $\overline{AC},$ and $\overline{BC},$ as shown below. If AB = 3 and BC = 4, then find AC.

Vxrtate Feb 11, 2024

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24

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+1756

perimeter

The perimeter of the triangle below is an integer. What is the smallest possible value of the perimeter? (Assume that the triangle is non-degenerate.) read more ..

bader Feb 11, 2024

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26

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+1341

Algebra

Consider the two expressions $1$ and $\frac{2x+3}{2x+3}.$
a) Show that the two expressions represent equal numbers when $x=10.$
b) Explain why these two expressions do not represent equal numbers when $x=-\dfrac32.$
c) Show that these read more ..

kittykat Feb 11, 2024

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19

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+400

Quadratic Roots

Let $a$ and $b$ be the roots of the quadratic $x^2 - 5x + 3 = 2x^2 + 14x + 8.$ Find the quadratic whose roots are 1/(a + 1) and 1/(b + 1).

omgitsrne Feb 11, 2024

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26

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+400

Quadratic equation

Fill in the blanks to make a quadratic whose roots are 5 and -5.
x^2 + ___x + ____

omgitsrne Feb 11, 2024

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