Thales of Miletus was a Greek mathematician who's work predates that of Euclid and Pythagoras.There are a number of theorems associated with his name -one is the Intercept Theorem for the ratios … [Read more...] about Thales’ Theorem
Arcs, Angles, and Sectors
An arc is a curved line segment that makes up part of the circle. The end-points of the arc on the circle's circumference defines two arcs, one in each direction.
If the two points lie at the ends of a diameter, the two arcs will be the same size. Otherwise, there will be one large arc called the major arc, and the smaller one the minor arc.
If we draw lines from the center of the circle to the end-points of the arc (these lines are both radii), we will define an angle called a Central Angle. If we draw chords from a point on the circle to each of the endpoints of the arc, we will define an angle called an Inscribed angle.
The Inscribed Angle's measure is half that of the central angle of the same arc, as we will prove in the problem set.
The area between an arc and the two radii lines from the center of the circle to the arc's end-points is called a sector.
Now that we've explained the basic concept of arcs, angles and sectors in geometry, let's scroll down to work on specific geometry problems relating to this topic.
Congruent circles have the same radius length.ProblemTwo congruent circles with radius 1 unit overlap, with the overlapping arc, AB, measuring π/3 units. Find the distance between the centers … [Read more...] about Distance Between the Centers of Overlapping Congruent Circles
If we draw lines from the center of the circle to the end-points of an arc on the perimeter of a circle, (these lines are both radii), we will define an angle called a Central Angle.If we draw … [Read more...] about The Inscribed Angle Theorem
An arc is a part of the circle's circumference. A circle measures 360°, so the length of an arc that is the entire circle (an arc measuring 360°) is simply the circle's circumference, given by … [Read more...] about How to Find the Length of an Arc in a Circle