A circle has the following equation: $ x^2-8ax+y^2+10ay=-5a^2 $ Point O is its center and is in the second quadrant ($$ a\neq0 $$) Use the completing the square method to find the center of the circle and its radius in terms of $$ a $$.

$$ O(4a,-5a),\hspace{4pt}R=-6a $$

$$ O(4a,5a),\hspace{4pt}R=6a $$

$$ O(4a,10a),\hspace{4pt}R=6a $$

$$ O(4a,-5a),\hspace{4pt}R=6a $$

A circle has the equation: $$ x^2-6x+y^2-4y=7 $$ Use the completing the square method to find the center of the circle and its radius.

$$ (3,2),\hspace{6pt} R=\sqrt{20} $$

$$ (3,-2),\hspace{6pt} R=\sqrt{20} $$

The Parts of a Circle - Examples, Exercises and Solutions

Understanding The Parts of a Circle

Complete explanation with examples

Circuit Components

Diagram of a circle illustrating geometric components: center 'M,' chord AB, secant line AF, arc AC, and radii MD and ME. The image highlights the relationships between chords, secants, and arcs in circle geometry

$AB$ chord
$AC$ arc
$DME$ central angle is $2$ times larger than inscribed angle $DFE$ – both intercepting the same arc

Detailed explanation

Practice The Parts of a Circle

Test your knowledge with 6 quizzes

Calculate the length of the arc marked in red given that the circumference is 12.

Examples with solutions for The Parts of a Circle

Step-by-step solutions included

Exercise #1

In which of the circles is the point marked inside of the circle and not on the circumference?

Step-by-Step Solution

Let's remember that the circular line draws the shape of the circle, and the inner part is called a disk.

Therefore, in diagram B, the point is located in the inner part, meaning inside the disk.

Answer:

Video Solution

Exercise #2

Identify which diagram shows the radius of a circle:

Step-by-Step Solution

Remember that a radius is a line segment connecting the center of a circle to any point on the circle itself.

In drawing C we can see that the line coming from the center of the circle indeed connects to a point on the circle itself, while in the other drawings the lines don't touch any point on the circle.

Therefore, C is the correct drawing.

Answer:

Exercise #3

Identify which diagram shows the radius of a circle:

Step-by-Step Solution

Remember that a radius is a line segment connecting the center of the circle to a point that lies on the circle itself.

In drawing A, the line doesn't touch any point on the circle itself.

In drawing B, the line doesn't pass through the center of the circle.

We can see that in drawing C, the line that extends from the center of the circle is indeed connected to a point on the circle itself.

Answer:

Video Solution

Exercise #4

Where does a point need to be so that its distance from the center of the circle is the shortest?

Step-by-Step Solution

Let's remember that the circle is actually the inner part of the circumference, meaning the enclosed area within the frame of the circumference.

Therefore, a point whose distance is less than the radius from the center of the circle will necessarily be inside the circle.

Answer:

Inside

Exercise #5

A point whose distance from the center of the circle is _______ than the radius, is outside the circle.

Step-by-Step Solution

Let's remember that the circle is actually the inner part of the circumference, meaning the enclosed area within the frame of the circumference.

Therefore, a point whose distance is greater than the center of the circle will necessarily be outside the circle.

Answer:

greater

Continue Your Math Journey

Master The Parts of a Circle first, then advance to these related topics that build on your fraction skills

Topics Learned in Later Sections

Circle Distance from a chord to the center of a circle Chords of a Circle Central Angle in a Circle Arcs in a Circle Perpendicular to a chord from the center of a circle Inscribed angle in a circle Tangent to a circle Elements of the circumference Area of a circle The Circumference of a Circle How is the radius calculated using its circumference?

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Calculate the ratio between radii of two circles Calculating arc length Calculating parts of the circle Identifying and defining elements