Monthly Archives: April 2022

Geometry – Sides and Angles of Triangles

Posted on April 22, 2022 by kevin

As shown in the diagram below, in $\triangle{ABC}$, $\angle{B}\gt \angle{C}$, $AD$ is the bisector of the $\angle{BAC}$, $AE\perp BC$ at $E$. Prove that $\angle{DAE}=\dfrac{1}{2}(\angle{B}−\angle{C})$. 2. There are four points $A$, $B$, $C$, $D$ on the plane, such that any three … Continue reading →

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Geometry Challenge – 12

Posted on April 4, 2022 by kevin

Acute $\triangle{ABC}$ is inscribed inside circle centered at $O$. $P$ is on $BC$ and $AP\perp BC$, and $\angle{ACB}>\angle{ABC}$. Prove the following: $\angle{BAC}+\angle{OBC}=90^\circ$ $\angle{OAP}=\angle{ACB}-\angle{ABC}$ If $\angle{ACB}-\angle{ABC}\ge 30^\circ$, and $MB=MC$, then $MP\gt CP$ If $\angle{ACB}-\angle{ABC}\ge 30^\circ$, then $\angle{BAC}+\angle{POC}<90^\circ$ Click here for the … Continue reading →

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