In geometry, "circumscribed" means "to draw around." A circumscribed circle is a circle that is drawn around a polygon so that it passes through all the vertices of a polygon inscribed in it. All … [Read more...] about Circumscribed Circle

# 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.*

## Tangent-Secant Theorem

Using the Tangent-Chord Theorem, it is simple to prove the third theorem which provides a relationship between lines in circles - the Tangent-Secant Theorem (the other two being the Intersecting … [Read more...] about Tangent-Secant Theorem

## The Tangent-Chord Theorem

The Tangent-Chord Theorem states that the angle formed between a chord and a tangent line to a circle is equal to the inscribed angle on the other side of the chord: ∠BAD ≅ ∠BCA. Problem Prove … [Read more...] about The Tangent-Chord Theorem

## Intersecting Secants Theorem

In today's lesson, we will present a detailed, step-by-step proof of the Intersecting Secants Theorem, using properties of similar triangles. This is a fairly simple proof, so today's lesson will be … [Read more...] about Intersecting Secants Theorem

## Tangents to a circle and inscribed angles

Today we'll find the angles of a triangle formed by two tangent lines to a circle using inscribed angles, and theorems about the sum of angles in a polygon. In this geometry problem, we will … [Read more...] about Tangents to a circle and inscribed angles

## Tangent Line to a Circle

A line tangent to a circle is a line from a point outside the circle that touches the circle at exactly one point. At that point, the tangent line is perpendicular to the circle's radius and diameter, … [Read more...] about Tangent Line to a Circle

## Area of a Circle Inscribed in an Equilateral Triangle

We can use the properties of an equilateral triangle and a 30-60-90 right triangle to find the area of a circle inscribed in an equilateral triangle, using only the triangle's side … [Read more...] about Area of a Circle Inscribed in an Equilateral Triangle

## Congruent Chords are Equidistant from the Center

Chords that have an equal length are called congruent chords. An interesting property of such chords is that regardless of their position in the circle, they are all an equal distance from the … [Read more...] about Congruent Chords are Equidistant from the Center

## A Diameter that Bisects Two Chords

In today's geometry lesson, we will prove that if a diameter bisects two chords in a circle, the two chords are parallel to each other. We can do this this three ways, relying on the properties of … [Read more...] about A Diameter that Bisects Two Chords

## A Diameter Perpendicular to a Chord

We've shown that a diameter that bisects a chord is perpendicular to that chord. Here, we will prove the converse theorem. Problem In circle O, the diameter AB is perpendicular to a chord CD. … [Read more...] about A Diameter Perpendicular to a Chord