Monthly Archives: November 2022

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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2022 AMC 10B Problem 20

Posted on November 18, 2022 by kevin

Let $ABCD$ be a rhombus with $\angle{ADC}=46^{\circ}$, and let $E$ be the midpoint of $\overline{CD}$, and let $F$ be the point on $\overline{BE}$ such that $\overline{AF}$ is perpendicular to $\overline{BE}$. What is the degree measure of $\angle{BFC}$? (A) 110 (B) 111 (C) 112 (D) 113 (E) 114 Solution Draw the … Continue reading →

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Rotational Symmetry of Platonic Solids

Posted on November 13, 2022 by kevin

In 3D geometry, a Platonic Solid is a convex polyhedron with all its faces are congruent regular polygons. There are only 5 Platonic Solids, Tetrahedron, Cube, Octahedron, Dodecahedron, and Icosahedron. Rotational Symmetry is the property of a geometric shape has … Continue reading →

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MathCounts Geometry Exercise – 2

Posted on November 4, 2022 by kevin

A B C D E P ________ The area of $\triangle{ABC}$ is $1$. $BD:DC=2:1$, and $E$ is the midpoint of $AC$. $AD$ intersects $BE$ at point $P$. Find the area of quadrilateral $PDCE$. ________ Rectangle $ABCD$ is divided into 4 … Continue reading →