Category Archives: Geometry

AIME 2022 II – Problem 15

Posted on February 3, 2023 by kevin

Two externally tangent circles $\omega_1$ and $\omega_2$ have centers $O_1$ and $O_2$, respectively. A third circle $\Omega$ passing through $O_1$ and $O_2$ intersects $\omega_1$ at $B$ and $C$ and $\omega_2$ at $A$ and $D$, as shown. Suppose that $AB = … Continue reading →

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AIME 2017 I – Problem 15

Posted on December 31, 2022 by kevin

The area of the smallest equilateral triangle with one vertex on each of the sides of the right triangle with side lengths $2\sqrt{3}$, $5$, and $\sqrt{37}$ as shown, is $\dfrac{m\sqrt{p}}{n}$, where $m$, $n$, and $p$ are positive integers, and $m$, $n$, … Continue reading →

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MathCounts Geometry Exercise – 4

Posted on December 2, 2022 by kevin

________ In parallogram $ABCD$, $EF\parallel AC$. The area of $\triangle{AED}=72\ cm^2$. Find the area the shaded region in $cm^2$. ________ In parallelogram $ABCD$, $CE$ intersects with $DA$ at $F$. The area of $\triangle{BEF}$ is $4\ cm^2$. Find the area the … Continue reading →

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AMC 2022 10A Problem 25

Posted on November 20, 2022 by kevin

Let $R$, $S$, and $T$ be squares that have vertices at lattice points (i.e., points whosecoordinates are both integers) in the coordinate plane, together with their interiors.The bottom edge of each square is on the $x$-axis. The left edge $R$ … Continue reading →

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MathCounts Geometry Exercise – 3

Posted on November 18, 2022 by kevin

________ In $\triangle{ABC}$, $D$ is the midpoint of $BC$. $E$ is on $AC$ so that $AE=2\ EC$. The area of $\triangle{ABC}$ is $60\ cm^2$. Find the area of $\triangle{ABF}$ in $cm^2$. ________ The area of rectangle $ABCD$ is $36$. $E$ … Continue reading →

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