• Skip to primary navigation
  • Skip to main content
  • Skip to primary sidebar
Geometry Help
  • About
  • Privacy Policy
  • Contact Me
  • Terms of Service
  • Accessibility Statement
menu icon
go to homepage
search icon
Homepage link
  • About
  • Privacy Policy
  • Contact Me
  • Terms of Service
  • Accessibility Statement
×

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.

Circles in Geometry

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 Ccircle=2*π*r (where r is the radius) , and since the diameter, d, is 2 times r, we can also write Ccircle=d*π

A circle's area is given by the formula Acircle=π*r2

--
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.

bisecting chords

Chords that Bisect Each Other

circle with equal arcs

Equal Chords Have Equal Arcs

Tangent Line

Prove that the Tangent is Perpendicular to the Radius

Two Circles Inscribed in a Square

Two Circles Inscribed in a Square

intersecting chords

Angles of Intersecting Chords

circle inscribed in a quadrilateral

Circle Inscribed in a Quadrilateral

Circle inscribed in a square

A Circle Inscribed in a Square

Square Inscribed in a Circle

Square Inscribed in a Circle

Thales' theorem

Thales' Theorem

kite in a circle

Kite Inscribed in a Circle

concentric circles with secant

Concentric Circles Intersected by a Secant

common chord

Finding the Length of a Common Chord

common chord

Common Chord of Two Circles

overlapping circles

Distance Between the Centers of Overlapping Congruent Circles

perp bisectors

Circumscribed Circle

Tangent-secant

Tangent-Secant Theorem

tangent and chord

The Tangent-Chord Theorem

intersecting secants

Intersecting Secants Theorem

Geometry drawing of a circle with a triangle and tangents.

Tangents to a circle and inscribed angles

tangent line to a circle

Tangent Line to a Circle

  • Go to page 1
  • Go to page 2
  • Go to Next Page »

Primary Sidebar

About

Welcome to Geometry Help! I'm Ido Sarig, a high-tech executive with a BSc degree in Computer Engineering and an MBA degree in Management of Technology. I'm here to tell you that geometry doesn't have to be so hard! My goal with this website is to help you develop a better way to approach and solve geometry problems, even if spatial awareness is not your strongest quality. Read More…

Geometry Topics

  • Area of Geometric Shapes
  • Circles
    • Arcs, Angles, and Sectors
    • Chords
    • Inscribed Shapes
    • Tangent Lines
  • Lines and Angles
    • Intersecting Lines and Angles
    • Parallel Lines
    • Perpendicular lines
  • Pentagons and Hexagons
  • Perimeter of Geometric Shapes
  • Polygons
  • Quadrangles
    • Kites (Deltoids)
    • Parallelograms
    • Rectangles
    • Rhombus
    • Squares
    • Trapezoids
  • Triangles
    • Congruent Triangles
    • Equilateral Triangles
    • Isosceles Triangles
    • Pythagorean Theorem
    • Right Triangles
    • Similar Triangles
    • Triangle Inequalities

By accessing or using this website, you agree to abide by the Terms of Service and Privacy Policy.


Copyright © 2023