Monthly Archives: August 2021

Fun Math Puzzles – 1

Posted on August 17, 2021 by kevin

My calculator is broken, it only has two working buttons. One of them adds $1$ to the result and the other doubles it. What is the minimum number of presses needed to get to 2021? Click for the solution We … 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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