Category Archives: Geometry

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

MATHCOUNTS Exercises – 12

Posted on January 15, 2020 by kevin

In $\triangle{ABC}$, $\overline{AB}=5$, $\overline{AC}=6$, $\overline{BC}=7$. Square $BCED$ is drawn along the side of $\overline{BC}$, as shown in the following figure. Find the area of $\triangle{ADE}$. Click here for the hint. Hint Draw the altitude from $A$ of $\triangle{ABC}$ intersecting $\overline{BC}$ … Continue reading →

Posted in Geometry, MATHCOUNTS | Comments Off on MATHCOUNTS Exercises – 12

MATHCOUNTS Exercises – 11

Posted on January 11, 2020 by kevin

As shown in the following figure, a quarter circle is drawn in a unit square, and 3 smaller squares are inscribed inside the quarter circle. Find the total area of the 3 smaller squares. Click here for the hint. Hint … Continue reading →

Posted in Algebra, Geometry, MATHCOUNTS | Comments Off on MATHCOUNTS Exercises – 11

MATHCOUNTS Exercises – 9

Posted on January 5, 2020 by kevin

A unit cube is painted with 1 face in red, 1 face in green, 1 face in yellow, and 3 faces in blue color. How many unique ways to paint the cube? Click here for the solution. Solution There are … Continue reading →

Posted in Combinatorics, Geometry, MATHCOUNTS | Comments Off on MATHCOUNTS Exercises – 9

MATHCOUNTS Exercises – 4

Posted on December 26, 2019 by kevin

MATHCOUNTS 2016-2017 – 240 Circle $P$ is internally tangent to circle $O$ at $A$, as shown. $\overline{AC}$ and $\overline{BE}$ intersect at $F$, which is also the point of tangency between $\overline{BE}$ and circle $P$. $\overline{AD}$ and $\overline{BE}$ are diameters of … Continue reading →

Posted in Geometry, MATHCOUNTS | Comments Off on MATHCOUNTS Exercises – 4