This presentation introduces the properties and applications of circles. It covers topics like radius, diameter, circumference, area, equations of circles, tangents, normals, sectors, segments, and circle theorems. Real-world examples of circles are also discussed, such as their use in roller coasters, telescopes, and describing planetary orbits. The presentation concludes that circles have fundamental geometric properties and important applications across many fields, and understanding circles provides powerful problem-solving tools.

1. The Fascinating
World of Circles
Welcome to this presentation on the wonderful properties and
applications of circles. From geometry to real-life examples, we'll
explore all the interesting aspects of circles!
by Rishabh

2. Properties of a Circle
1 Radius and Diameter
Learn about the fundamental
components of a circle and
their relation to each other.
2 Chords and Arcs
Understand the different
segments that make up a
circle and their properties.
3 Circumference and
Area
Discover the formulas to
calculate the length of the
outer edge and the surface
area of a circle.

3. Equations of a Circle
1
Standard Form
Learn how to write the equation of a circle in standard
form and understand what each variable represents.
2
Center-Radius Form
Get a more intuitive understanding of the equation of
a circle by exploring its center point and radius.
3
General Form
Discover the most flexible way of writing the equation
of a circle, including when it's not centered on the
origin.

4. Tangents and Normals
Tangents to a Circle
Explore how to find the tangent line from an external point
and how to draw a tangent line to a circle from a point on
the circle.
Normals to a Circle
Discover how to draw the normal line to a circle from a
point on the circle and how to find the equations of
tangents and normals in different situations.

5. Sectors and Segments of a Circle
Sector of a Circle
Understand the definition of a sector and learn how to
find its area and arc length using radians and degrees.
Segment of a Circle
Explore the properties of a segment and understand how
to calculate its area and perimeter.

6. Applications of Circles in Real Life
Roller Coasters
Discover how the principles of
circles are used to create thrilling
roller coaster rides.
Telescope Mirrors
Learn how large telescope
mirrors are constructed using
segments of a circle to allow us
to explore the universe.
Planets and Orbits
Explore how circles and ellipses
are used to describe the orbits of
planets around the Sun.

7. Circle Theorems
1
Angle at the Center
Understand the relationship between the angle at the
center of a circle and the angles at the circumference
that it subtends.
2
Angles in a Semicircle
Discover the important relationship between angles in
a semicircle and how it can be used to solve
problems.
3
Secants and Tangents
Explore the properties of angles formed by secant
and tangent lines and how they can be applied in
real-life situations.

8. Conclusion and Summary
Key Takeaways
• Circles have fundamental properties that allow us
to understand their structure and behavior.
• Circles have important applications in fields such
as physics, engineering, and astronomy.
• Circle theorems provide us with powerful tools to
solve problems involving circles.
What's Next?
Now that you've learned all about circles, you can
explore more advanced topics such as conic sections,
trigonometry, and calculus.