Category Archives: Geometry

MATHCOUNTS Exercises – 20

Posted on February 1, 2020 by kevin

Given an equilateral $\triangle{ABC}$ shown below, $AB=BC=CA=1$, point $D$ and $E$ trisect side $AB$, point $F$ and $G$ trisect side $BC$, point $H$ and $I$ trisect side $CA$. Two overlapping equilateral triangles are formed by linking various intersect points. Find … Continue reading →

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MATHCOUNTS Exercises – 17

Posted on January 28, 2020 by kevin

In rectangle $ABCD$, shown here, point $M$ is the midpoint of side $BC$, and point $N$ lies on $CD$ such that $DN:NC=1:4$. Segment $BN$ intersects $AM$ and $AC$ at points $R$ and $S$, respectively. If $NS:SR:RB=x:y:z$, where $x$, $y$ and … Continue reading →

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MATHCOUNTS Exercises – 16

Posted on January 26, 2020 by kevin

A semicircle and a circle are placed inside a square with sides of length 4 cm as shown. The circle is tangent to two adjacent sides of the square and to the semicircle. The diameter of the semicircle is a … Continue reading →

Posted in Circles in a Square, Geometry, MATHCOUNTS | Comments Off on MATHCOUNTS Exercises – 16

MATHCOUNTS Exercises – 15

Posted on January 22, 2020 by kevin

How many distinct unit cubes are there with two faces painted red, two faces painted green and two faces painted blue? Two unit cubes are considered distinct if one unit cube cannot be obtained by rotating the other. SOURCE: 2014 … Continue reading →

Posted in Combinatorics, Geometry, MATHCOUNTS | Comments Off on MATHCOUNTS Exercises – 15

MATHCOUNTS Exercises – 13

Posted on January 16, 2020 by kevin

In regular pentagon $ABCDE$, point $M$ is the midpoint of side $AE$, and segments $AC$ and $BM$ intersect at point $Z$. If $ZA = 3$, what is the value of $AB$? Express your answer in simplest radical form. Source: MATHCOUNTS … Continue reading →

Posted in Algebra, Geometry, MATHCOUNTS | Comments Off on MATHCOUNTS Exercises – 13