Category Archives: Geometry

Storing Cans on Shelf

Posted on November 8, 2021 by kevin

If cans can be placed on top of the one another straight up, how many cylindrical cans $4$ inches in diameter and $6$ inches high can be stored on a shelf $2$ feet wide and $6$ feet long if the … Continue reading →

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Geometry Challenge – 8 ⭐

Posted on October 16, 2021 by kevin

In unit square $ABCD$, point $E$ and $F$ are located on edge $CD$, with $E$ closer to $D$ and $F$ closer to $C$. Line $BE$ and $AF$ intersect at $G$, forming two triangles: $\triangle{ABG}$ and $\triangle{EFG}$. Find the minimum value … Continue reading →

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Geometry Challenge – 7 ⭐

Posted on August 4, 2021 by kevin

In parallegram $ABCD$, point $E$ and $F$ are on side $AB$ and $AD$ respectively. $EF$ intersects diagonal $AC$ at $G$. Show that $\dfrac{AB}{AE}+\dfrac{AD}{AF}=\dfrac{AC}{AG}$. Click for the hint

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Geometry Challenge – 6 ⭐⭐⭐⭐⭐

Posted on August 4, 2021 by kevin

In parallelogram $ABCD$, diagonal $AC$ tangents the incircle of $\triangle{ABC}$ at $P$. Let $r_1$ and $r_2$ be the radii of incircles of $\triangle{ADP}$ and $\triangle{DCP}$ respectively. 1. Prove that $\dfrac{r_1}{r_2}=\dfrac{AP}{CP}$ 2. If $AD=PD$, and $\dfrac{AD+CD}{AC}=p$, where $p>1$, prove that $\dfrac{r_1}{r_2}=1+\dfrac{1}{p}$. … Continue reading →

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Geometry Challenge – 5 ⭐⭐

Posted on July 26, 2021 by kevin

Point $E$ is inside square $ABCD$ and on the semi-circle with its radius as $AD$. If $DE=10$, find the area of $\triangle{CDE}$.

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