maximum

256 Questions
128 Answers

0

36

1

+818

bisectors

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.</ lire plus ..

maximum 13 oct. 2023

0

82

1

+818

help with 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. lire plus ..

maximum 13 oct. 2023

0

65

1

+818

help 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 $BE$.

maximum 12 oct. 2023

0

136

0

+818

angle bisectors

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 $AMN$.

maximum 12 oct. 2023

0

88

1

+818

points on a circle

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

maximum 12 oct. 2023

0

127

0

+818

help plz

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 lire plus ..

maximum 12 oct. 2023

0

109

0

+818

domain

If $f(x)$ is a function whose domain is $[-8,8]$, and $g(x)=f\left((x^2 - 2)/(x + 1)\right)$, then the domain of $g(x)$ is an interval of what width?

maximum 12 oct. 2023

+1

73

1

+818

I need help

Find the domain of the function \[f(x)=\sqrt{1-\sqrt{2+\sqrt{3+\sqrt{x}}}}.\]

maximum 9 oct. 2023

+1

102

2

+818

help with function

Find the domain of the function $$f(x) = \frac{\sqrt{x}}{\sqrt{x^2}}.$$ Express your answer as an interval or as a union of intervals.

maximum 9 oct. 2023

0

120

0

+818

need help

Find the domain of the function $$f(x) = \frac{1}{x+8} + \frac{1}{\sqrt{x - 8}} + \frac{1}{\sqrt{8 - x}}.$$ Express your answer as a union of intervals.

maximum 9 oct. 2023

+818

-1

Do not post AoPS homework.

maximum20 janv. 2025