GEOMETRY TUTOR DRAWING CIRCLES IN MISSION VIEJO
Last Updated on September 30, 2020 by A Plus In-Home Tutors
If you take GEOMETRY in MISSION VIEJO, you will eventually hit that dreaded section on circles.
As a GEOMETRY tutor, I see many students struggling with circles. But once you know the basics, working with circles can be enjoyable.
Geometry Basics: Parts of a Circle
Circles largely present a challenge to students because of their differently named parts compared to other common shapes like triangles and quadrilaterals. When students hear terms like “radius” and “circumference,” the first instinct might be overwhelming confusion.
But the most important parts of a circle aren’t as overwhelming as they sound.
The origin is simply the center of a circle.
The radius marks the distance from the origin to the circle’s edge.
Radii is just the plural form of radius.
The diameter runs through the origin from one side of a circle to the other – or, two radii lined side-to-side.
The circumference is just a fancy name for “perimeter,” or the distance around a circle.
And finally, pi ( is the special irrational number that enters both the circumference and area formulas of a circle.
Which brings us to the next set of GEOMETRY basics.
Geometry Basics: Formulas of a Circle
Often in GEOMETRY students will confuse the two primary formulas used for circles: circumference and area. Memorizing these formulas is key to success in GEOMETRY.
Both formulas use pi ( . Both formulas use the radius (r). But there are major differences between the two formulas, too.
Circumference of a circle:
To find the circumference of a circle, you multiply 2 times times the radius r. Another variation of this formula includes the diameter d:
Circumference of a circle:
Since 2 radii amount to the same distance as a single diameter, you can simply replace 2r with a single d. This formula is especially useful when given an example that includes the circle’s diameter, not its radius.
In GEOMETRY, simply use whichever formula is more convenient! If given the radius, use the first circumference formula; if given the diameter, employ the second.
Finally, there is the area formula. Unlike the circumference formula, the area formula for a circle only has one “version,” so it must be memorized straightforwardly:
Area of a circle:
Just remember, in GEOMETRY, you never square the radius or the diameter in the circumference formula – only with the area. In the circumference formula, you’re either multiplying by 2r or d. With area, on the other hand, you’re always multiplying by the radius r squared.
So, if you’re given the diameter and need to find the area of the circle, simply cut your diameter in half to find the radius r. Square r and multiply by , and you’re set to go!
Remember these GEOMETRY basics, and circles will serve you significantly more simply.