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A quadrilateral is inscribed when all vertices belong to the circumference.
📌 Important property:
\( \text{soma dos ângulos opostos} = 180^\circ \)
📌 Example:
If an angle measures\( 110^\circ \), then the opposite angle is: \( 180^\circ - 110^\circ = 70^\circ \)
What are rational numbers?
They are numbers that can be written in fraction form:
\( \frac{a}{b}, \quad b \neq 0 \)
Examples:
\( \frac{3}{4}, -2, 0{,}5, -\frac{7}{3} \)
valor absoluto
The valor absoluto represents the distance to zero:
\( |a| = a \) se \( a \geq 0 \)
\( |a| = -a \) se \( a < 0 \)
Examples:
\( |5| = 5 \)
\( |-5| = 5 \)
Simétrico
The ..know more
Word that replaces or accompanies a noun, avoiding repetition and indicating person, possession, quantity, or relation.
Ex.: ele, aquele, meu, ninguém.
Subclasses de pronomes
Pronome pessoal
Refers to the persons in speech: 1ª, 2ª ou 3ª pessoa.
- Formas tónicas: used alone or for emphasis (mim, ti, ele, nós).
- Formas átonas: used attached to the verb (me, ..know more
The Rubik's Cube, created by Hungarian architect and architecture professor Ernő Rubik in 1974, has become one of the world's most popular puzzles and a true cultural icon. Originally invented by Rubik as a teaching tool to teach his students about geometry and spatial transformations, it quickly became a worldwide challenge.
The 3x3x3 cube, the best-known version, has around 43 quintillion possible ..know more
December 15th Zamenhof day, in honor of Ludwig Zamenhof, the creator of Esperanto born in 1859. Ludwig Zamenhof was a Polish doctor and linguist, born in a multicultural region of Poland, where various ethnicities and languages coexisted, but also often conflicted. Noting linguistic and cultural barriers, Zamenhof envisioned a neutral, easy-to-learn language that could serve as a universal ..know more
In 1950, Brazil was hosting the World Cup and everything seemed perfect:
The country had a very strong team
They were playing at home
The Maracanã stadium was packed with around 200,000 people
👉 There was no final like today — it was a final group stage.
The last match was practically a “final”:
Brazil vs Uruguay
What did Brazil need?
Very simple:
✔️ ..know more
Frase ativa e frase passiva
✔ Frase ativa: the subject performs the action.
Ex.: O João leu o livro.
✔ Frase passiva: the subject receives the action.
Ex.: O livro foi lido pelo João.
👉 Tip:
Sujeito da ativa → agent (passive)
CD da ativa → subject (passive)
Discurso direto e indireto
✔ Discurso direto: exact words are reproduced.
Ex.: ..know more
Love is not just a feeling; it has a chemical basis in the brain. The most famous hormone associated with love is oxytocin, often called the “love hormone.” It is released during closeness, hugging, affection, and intimacy, strengthening emotional bonds and creating feelings of trust and attachment.
But how long does it take for the brain to fall in love? Studies show that intense attraction can ..know more
Who was Stanislav Petrov?
Stanislav Yevgrafovich Petrov was an officer in the Soviet Air Force, born in 1939 in the former Soviet Union. He was neither a politician nor a high-ranking military leader. He was an engineer trained to analyze nuclear early-warning systems, an ordinary man within an extremely dangerous Cold War machine.
What was his real position?
Petrov was ..know more
Did you know that platforms already exist where artificial intelligences talk only to each other, with no human participation?
One example that recently went viral is Moltbook, described as a “Reddit for AIs.” On it, bots create posts, comment, reply, and vote on each other in a fully autonomous way. There are no human users writing — only observing.
What intrigued the internet wasn’t just ..know more
Points within a game
Each game starts at 0, called “Love”.
The scoring goes: 0 → 15 → 30 → 40 → game.
If both players reach 40, it is called Deuce.
To win the game from Deuce, you need to win 2 consecutive points.
Games within a set
A set is won by the player who wins 6 games with at least a 2-game advantage.
Examples:
6-3 → normal win
6-5 ..know more
Origin of the Sphinx
The Great Sphinx of Giza, located near the pyramids of Khufu, Khafre, and Menkaure, is one of the oldest and most iconic sculptures in Egypt.
It is believed to have been built during the reign of Pharaoh Khafre (c. 2500 B.C.).
It has the body of a lion and the head of a human, possibly representing the pharaoh himself or a protective deity.
Original ..know more
Esther and Ruth: courage and faith
Esther and Ruth are examples of women who played central roles in the Bible, demonstrating courage, faith, and determination:
Esther became queen of Persia and risked her life to save the Jewish people from destruction (Book of Esther). Her story is an example of boldness, strategy, and faith in God, inspiring celebrations such as Purim.
Ruth, ..know more
Understand What a “Six-Pack” Really Is
Abdominal muscle: can be strengthened with specific exercises.
Abdominal fat: covers the muscles; even with strong abs, it needs to be reduced to show.
In other words, it’s not just about doing crunches all day.
Strategic Nutrition
Moderate calorie deficit: burning more energy than you consume helps reduce fat.
Enough ..know more
Lisbon is not just built above ground. Over more than two thousand years, different civilizations have constructed underground structures that remain hidden to this day.
Origin of the tunnels
Romans: drainage galleries, aqueducts, and sewers.
Islamic period: passages used for escape and supply.
Middle Ages: corridors under convents, churches, and palaces.
Purpose
Escape ..know more
Juan Pujol García (1912–1988), codename Garbo, was the spy who fooled Hitler on his own. He created a fictional network of 27 agents that never existed, sending detailed reports with deliberately human errors. His cunning changed the course of the war.
Who he was
• Spanish, ordinary childhood
• Initially uninterested in politics
• Offered his services to the British and then deceived ..know more
Virginia Hall (1906–1982) was an American agent during World War II who defied every stereotype. A woman, a foreigner, and with a prosthetic leg — which she nicknamed “Cuthbert” — she embodied everything the Nazis underestimated. Even so, she became the most dangerous agent in occupied France.
Who she was
• American, former diplomatic service candidate
• Lost part of her leg in an accident
• ..know more
Eleven was almost a boy
In the early drafts by the Duffer Brothers, the main character was written as a different gender. By changing Eleven into a girl, the series gained a stronger emotional layer: apparent fragility versus extreme power, as well as themes of motherhood, friendship, and identity.
The Upside Down came before the story
Unlike the usual process, the creators ..know more
The Rossio Statue
Although everyone believes the statue represents D. Pedro IV, there is a myth that it was repurposed from another historical figure.
To prevent anyone from noticing, it was placed at the top of the column, out of public view.
This shows how urban legends can arise from seemingly small historical details.
Lisbon
Some buildings in the city date ..know more
The Apocalypse
Many viewers spend the series trying to discover the virus’s origin, but Robert Kirkman, the creator, made it clear: it doesn’t matter. The focus is on humans — how people behave when society disappears, when there are no laws, comfort, or security. The virus is just a catalyst that reveals who people really are.
The Infection
The famous reveal that anyone ..know more
1. A universe built by players
Since 2006, Roblox has allowed anyone to create and play unique worlds. Thousands of games are made by the community, from epic adventures to wacky simulations.
2. A billion-dollar community
Some creators have earned millions from their games, turning fun into a business. Roblox’s economy is real and very active.
3. Engaging events
Constant ..know more
In the center of Lisbon, in Rossio Square, stands a column crowned by a statue attributed to Dom Pedro IV. At first glance, it appears to be a clear symbol of Portuguese liberalism. However, the story behind the sculpture is more curious than it seems.
Origin of the statue
Inaugurated in 1874
Officially dedicated to Dom Pedro IV
Cast in bronze and placed atop a tall column
The ..know more
Beer Was Safer Than Water
In the Middle Ages, water was often contaminated, while boiling beer wort killed bacteria.
Children and adults drank “small beer” daily as a safe and nutritious beverage.
This shows how beer was an essential part of the diet and public health at the time.
The Monks
During Lent, monks brewed strong and nutritious beers.
The drink ..know more
The Pico Paraná, at 1,877 meters, is the highest point in southern Brazil and is located in the Serra do Mar, between the municipalities of Antonina and Campina Grande do Sul, in Paraná. Its geological formation dates back to the Precambrian period, millions of years ago, when tectonic uplift and erosion processes formed its igneous and granitic rocks. The name “Paraná” comes from the Tupi language ..know more