Author Archives: kevin

MATHCOUNTS Exercises – 14

Posted on January 19, 2020 by kevin

Lisa wants to use her calculator to square a two-digit positive integer, but she accidentally enters the tens digit incorrectly. When she squares the number entered, the result is 2340 greater than the result she would have gotten had she … Continue reading →

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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 →

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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 →

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Circles in a Square – Part 11

Posted on January 11, 2020 by kevin

8 semi-circles are drawn along the side lines inside of a unit square as shown in the following figure, with another circle centered at the center of the square and tangent to all of 8 semi-circles. What is the area of … Continue reading →

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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 →