maximum

260 Questions
128 Answers

0

1

5

+835

Geometry

The area of square ABCD is 36. E is a point on \overline{CD} such that CE=2ED. F is the intersection of AB and CD. Find [DEF].

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maximum 04.09.2026

0

1

1

+835

Geometry

In \triangle ABC, shown here, \overline{AB} and \overline{AC} have each been divided into four congruent segments. What fraction of triangle ABC is shaded? Express your answer as a common fraction.

maximum 04.09.2026

0

1

1

+835

Geometry

In the diagram, BD = 2 \cdot CD and CF = FB. Find the length AE.

maximum 04.09.2026

0

1

1

+835

Geometry

In the diagram, \triangle ABC \cong \triangle BFA. Find \frac{AB}{BC}.

maximum 04.09.2026

0

77

1

+835

Algebra

Let a and b be the solutions to 7x^2 + x - 5 = 6x^2 - 11x - 2. Compute (a - 4) + (b - 4).

maximum 11.04.2024

0

70

1

+835

Geometry

In triangle $PQR,$ $M$ is the midpoint of $\overline{PQ}.$ Let $X$ be the point on $\overline{QR}$ such that $\overline{PX}$ bisects $\angle QPR,$ and let the perpendicular bisector of $\overline{PQ}$ intersect $\overline{PX}$ at $Y.$ If PQ = 36, PM = 22, mehr ..

maximum 07.04.2024

0

5

1

+835

Hexagon

Let $IJKLMN$ be a hexagon with side lengths $IJ = LM = 3,$ $JK = MN = 3,$ and $KL = NI = 3$. Also, all the interior angles of the hexagon are equal. Find the area of hexagon $IJKLMN$.

maximum 28.01.2024

0

76

1

+835

Probability

A member of the junior varsity swim team will be elected as President. Each member is equally likely to be elected. The probability that a sophomore is elected is times the probability that a freshman is elected. Everyone on the junior varsity mehr ..

maximum 16.01.2024

0

84

1

+835

Counting

Find the number of positive integers that satisfy both the following conditions:
- Each digit is a 1 or a 2 or a 3
- The sum of the digits is 5

maximum 16.01.2024

0

100

0

+835

Counting

We call a number cozy if every digit in the number is either even or next to an even digit. For example, a number is cozy if every digit in the number is either a 2 or next to a 2. For example, the number 222, 72, 45, and 810 and mehr ..

maximum 18.12.2023

+835

-1

Do not post AoPS homework.

maximum20.01.2025