Circles are the most perfect and symmetrical shapes in nature. From the wheels of a car to the orbits of planets, the math of circles is essential for engineering and astronomy.
A circle is full of hidden relationships. An 'inscribed angle' is formed when two lines meet on the edge of the circle. The Inscribed Angle Theorem states that an inscribed angle is exactly half of the central angle that subtends the same arc.
A common mistake is assuming that any angle inside a circle follows the theorem. The vertex MUST be exactly on the circumference for it to be an inscribed angle!
Move the point on the edge of the circle to see how the inscribed angle stays exactly the same, as long as it shares the same arc!
Test your knowledge of circle properties!
Thales of Miletus, an ancient Greek philosopher, was one of the first to prove that an angle inscribed in a semicircle is always a right angle. This theorem (Thales's Theorem) is considered one of the very first mathematical discoveries in human history!