Monthly Archives: July 2021

Elon Musk’s Interview Question

Posted on July 27, 2021 by kevin

It is known that Telsa/SpaceX CEO Elon Musk would ask a job candidate some brain teaser questions during an interview, such as the following: You’re standing on the surface of the earth. You walk one mile south, one mile west, … 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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Geometry Challenge – 4 ⭐⭐

Posted on July 23, 2021 by kevin

$AB$ is the diameter of the circle center at $O$. $CD$ is tangent to the circle at $D$ and $AB\parallel CD$. $AC$ intersects the circle at $E$ and $AE=CE$. Find $\angle{ACD}$.

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Geometry Challenge – 3 ⭐⭐⭐

Posted on July 23, 2021 by kevin

A fixed point $Q$ lies on the bisector of $\angle{P}$. A moving point $A$ lies on one side of $\angle{P}$, with line $AQ$ intersecting the other side of $\angle{P}$ at point $B$. Show that $\dfrac{1}{PA}+\dfrac{1}{PB}$ is a constant.

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Mass Points Exercises

Posted on July 22, 2021 by kevin

(AIME 2011) In triangle $ABC, AB=\dfrac{20}{11}AC.$ The angle bisector of $\angle A$ intersects $BC$ at point $D$, and point $M$ is the midpoint of $AD$. Let $P$ be the point of intersection of $AC$ and $BM$. Find $\dfrac{CP}{PA}$. SolutionWithout loss … Continue reading →

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