Problems

Which triangle has the largest area? The dots form a regular grid.

What is the ratio between the red and blue area? All shapes are semicircles.

In a parallelogram $ABCD$, point $E$ belongs to the side $CD$ and point $F$ belongs to the side $BC$. Show that the total red area is the same as the total blue area:

The figure below is a regular pentagram. What is larger, the black area or the blue area?

A circle was inscribed in a square, and another square was inscribed in the circle. Which area is larger, the blue or the orange one?

In a square, the midpoints of its sides were marked and some segments were drawn. There is another square formed in the centre. Find its area, if the side of the square has length $10$.

In a parallelogram $ABCD$, point $E$ belongs to the side $AB$, point $F$ belongs to the side $CD$ and point $G$ belongs to the side $AD$. What is more, the marked red segments $AE$ and $CF$ have equal lengths. Prove that the total grey area is equal to the total black area.

Doctor Smith gave out 2006 miracle tablets to four sick animals. The rhinoceros received one more tablet than the crocodile. The hippopotamus got one more tablet than the rhino. The elephant got one more tablet than the hippo. How many tablets did the elephant have to eat?

There are two numbers $x$ and $y$ being added together. The number $x$ is less than the sum $x+y$ by 2000. The sum $x+y$ is bigger than $y$ by 6. What are the values of $x$ and $y$?

The digits of a 3 digit number $A$ were written in reverse order and this is the number $B$. Is it possible to find a value of $A$ such that the sum of $A$ and $B$ has only odd numbers as its digits?