There are several theorems related to chords and radii or diameters that connect to them. In today's lesson, we will first prove that a diameter that bisects a chord is perpendicular to that chord and … [Read more...] about A Diameter Bisecting a Chord

# Circles

In geometry, a circle is defined as the collection of all points that are the same distance from one point, which is the center of the circle.

The distance from the center of the circle to any point on the circle is called the radius, and commonly written 'r'.

If we draw a line from one point on the circle, through its center and on to another point on the circle, directly across from the first point, that line's length will be 2 times r, and is called the circle's diameter, 'd'. d= 2*r

A circle is a geometric shape completely defined by its radius- knowing the radius we can calculate the circle's area, and its circumference.

A circle's circumference, C, is C_{circle}=2*π*r (where r is the radius) , and since the diameter, d, is 2 times r, we can also write C_{circle}=d*π

A circle's area is given by the formula A_{circle}=π*r^{2}

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*Now that we've explained the basic concept of circles in geometry, let's scroll down to work on specific geometry problems relating to this topic.*

## Radius of a Circle with an Inscribed Triangle

In today's lesson, we will learn how to find the radius of a circle with an inscribed triangle. Many geometry problems involve a triangle inscribed in a circle, where the key to solving the … [Read more...] about Radius of a Circle with an Inscribed Triangle

## Inscribed Shapes: Opposing Angles of a Quadrangle Inscribed in a Circle

In today's lesson, we will prove that in a quadrangle inscribed in a circle, the opposing angles are supplementary. Not all quadrangles can be inscribed in a circle. Intuitively, if we think of a … [Read more...] about Inscribed Shapes: Opposing Angles of a Quadrangle Inscribed in a Circle

## Polygon Inscribed in a Circle

We will solve most problems involving polygons inscribed in a circle by using theorems related to inscribed angles, as the vertices of the polygons form inscribed angles. Problem An irregular … [Read more...] about Polygon Inscribed in a Circle

## Intersecting Chords Theorem

The intersecting chords theorem states that when two chords intersect at a point, P, the product of their respective partial segments is equal. In other words: AP*PB=CP*PD Problem Prove that … [Read more...] about Intersecting Chords Theorem

## Proving the Inscribed Angle Theorem

In today's lesson, we will prove the Inscribed Angle Theorem. We will show that the Inscribed angle's measure is half that of the central angle of the same arc. If we draw lines from the center of … [Read more...] about Proving the Inscribed Angle Theorem

## The Two Tangent Theorem

The two tangent theorem states that if we draw two lines from the same point which lies outside a circle, such that both lines are tangent to the circle, then their lengths are the same. We will now … [Read more...] about The Two Tangent Theorem

## Arc Length Formula

In today's lesson, we will show a simple formula for finding the length of an arc in a circle. An arc is a part of the circle's circumference. A circle measures 360°, so the length of an arc that … [Read more...] about Arc Length Formula