Author Archives: kevin

Geometry Probability – 3

Posted on September 18, 2024 by kevin

Two points are randomly and uniformly selected from the interior of a circle. The center of the circle and the two points joined together form a triangle. What is the probability that the triangle is acute? Click here for the … Continue reading →

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A MATHCOUNTS Problem with Multiple Answers 🙂

Posted on August 19, 2024 by kevin

The following is MATHCOUNTS 2012 National Competition Sprint Round Problem 22: In circle $O$, shown, $OP=2$ units, $PL=8$ units, $PK=9$ units and $NK=18$ units. Points $K$, $P$ and $M$ are collinear, as are points $L$, $P$, $O$ and $N$. What … Continue reading →

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Geometry Probability – 2

Posted on August 5, 2024 by kevin

An iron rod of $1$ foot long is cut into three segments with random length. (1) What is the probability that the three segments form a triangle? (2) What is the probability that the three segments form an acute triangle? … Continue reading →

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Geometry Probability – 1

Posted on July 22, 2024 by kevin

3 random points are chosen independently on a circle. What is probability that they form an acute triangle? Click here for the solution. Solution: This problem is equivalent to the following: Two cuts are randomly made on a line of … Continue reading →

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Algebra/Geometry Challenge – 1

Posted on June 17, 2024 by kevin

As shown in the following figure, $D$, $E$, $F$ are on the sides of $\triangle{ABC}$, $AC$, $AB$, and $BC$ respectively. $AE=BE$, $AD=6$, $CD=7$, $BF=2$, $CF=9$. $DEFG$ is a square. The length of $AB$ can be expressed as $\ \ \ … Continue reading →