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Category Archives: Geometry
Geometry Probability – 3
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
Posted in Algebra, Calculus, Geometry, Probability
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A MATHCOUNTS Problem with Multiple Answers 🙂
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
Posted in Fun Math Facts, Geometry, MATHCOUNTS, Trigonometry
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Geometry Probability – 1
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
Algebra/Geometry Challenge – 1
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
Circles in a Square – Part 12
As shown in the figure, $ABCD$ is a square, $E$ is the mid-point of $AB$. The circle with its center at $H$ is tangent with $AD$, $AE$ and $DE$. The circle with its center at $F$ is tangent with $BC$, … Continue reading
Posted in Circles in a Square, Geometry
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