Monthly Archives: January 2025

Geometry Challenge – 17

Posted on January 12, 2025 by kevin

Let $D$ be an interior point inside equilateral $\triangle{ABC}$, so that $\angle{BDC}=150^\circ$. Prove that the line segment $AD$, $BD$ and $CD$ are the sides of a right triangle. Click here for the proof. Proof: Rotating $\triangle{ADC}$ counter-clock-wise around $C$ by … Continue reading →

Posted in Geometry | Comments Off on Geometry Challenge – 17

Algebra Challenge – 5

Posted on January 5, 2025 by kevin

Find the real solutions for the following equations: $$a^2+b^2\ \ \ \ \ \ \ \ \ \ \ \ \ =1\tag{1}$$ $$b^2+c^2+\sqrt{3}bc=1\tag{2}$$ $$c^2+a^2+\ \ \ \ \ ca=1\tag{3}$$ Click here for the solution. Solution: If $c=0$, based on equation … Continue reading →

Posted in Algebra | Comments Off on Algebra Challenge – 5