Sunaina thinks absurd

 These problems are INMO~ish level. So trying this would be a good practice for INMO!  Let $ABCD$ be a quadrilateral. Let $M,N,P,Q$ be the midpoints of sides $AB,BC,CD,DA$. Prove that $MNPQ$ is a parallelogram. Consider $\Delta ABD$ and $\Delta BDC$ .Note that $NP||BD||MQ$. Similarly, $NM||AC||PQ$. Hence the parallelogram. In $\Delta ABC$, $\angle A$ be right. Let $D$ be the foot of the altitude from $A$ onto $BC$. Prove that $AD^2=BD\cdot CD$. Note that $\Delta ADB\sim \Delta CDA$. So by similarity, we have $$\frac{AD}{BD}=\frac{CD}{AD}.$$ In $\Delta ABC$, $\angle A$ be right. Let $D$ be the foot of the altitude from $A$ onto $BC$. Prove that $AD^2=BD\cdot CD$. Let $D\in CA$, such that $AD = AB$.Note that $BD||AS$. So by the Thales’ Proportionality Theorem, we are done! Given $\Delta ABC$, construct equilateral triangles $\Delta BCD,\Delta CAE,\Delta ABF$ outside of $\Delta ABC$. Prove that $AD=BE=CF$. This is just congruence. N...

I had to learn basic things about vectors. So thought why not write a blog post :P?  Also special thanks to papa 💫  So here we go.. PHYSICAL QUANTITY:- A quantity that can be measured and expressed in units. We have two types of Physical Quantity Scalar:- A physical quantity that has only magnitude. Example: Mass, speed. Vectors:- A physical quantity that has both magnitude and direction. Example: Displacement, velocity.  Now, what are vectors? VECTORS:- A physical quantity that has both magnitude and direction. In geometry, a vector is a directed line segment, whose length is the MAGNITUDE of the vector and the arrow indicating the DIRECTION. The MAGNITUDE of a vector $(\vec{A})$ is the absolute value of a vector and is indicated as $\boxed{|\vec{A}|}.$ REPRESENTATION OF VECTORS:- A vector pointing from $A$ to $B$ is written as $\vec{AB}.$ We usually define a single point $O$ as the ORIGIN. Then we associate every point $P$ with the vector $\vec{OP}$ or $\vec{P}$ MAGNIT...