Chord Length

MATH 5 Q3 W4

Identifying Terms Related to a Circle and Drawing Circles with Different Radii Using a Compass

Circles are everywhere! Some of the real-world examples of circle -shaped objects are the sides around the following:

• the wheel of a bicycle

• coin

• dinner plate

• wall clock

• Ferris wheels

A circle is an important shape in the field of geometry.

A circle is a round-shaped figure that has no corners or edges. In geometry, a circle can be defined as a closed, two-dimensional curved shape.

• A circle is a basic 2D shape which is measured in terms of its radius. The different parts of a circle are explained below in detail.

• A circle is the set of all points in a plane with the same distance from a certain point. This point is called the center of the circle.

Refer to the figures:

* A is the center and the name of the circle is circle A.

* Chord a line segment joining two points on the circle. In circle A, segments CE and BG are chords.

* Diameter is a chord that connects two points on the circle. Every diameter is a chord. In circle A, segment BF is a diameter. The diameter goes straight across the circle, through the center.

* The circumference is the distance once around the circle.

 

* Radius is a line segment from the center of the circle to any point on the circle. The radius of a circle is one-half the diameter. In circle A, segments AB, AF, AD and AH are radii.

* Central angle is an angle formed by two radii. In circle A, <BAD, <BAH and <HAF are central angles.

 

* Inscribed angle is an angle whose vertex is on the circle. In circle A, <FBG is an inscribed angle.

What do the following objects have in common? If you are asked to draw them perfectly, how will you do it?

• Wheel                     

• Cymbals   

• One-peso coin

• Eyeballs

• Manholes

Using your bare hands will not guarantee that you will be able to draw a perfect circle. In drawing a circle, we need a compass.

A compass is an instrument used in drawing circles.    

Here are the steps in drawing circles using a compass.

1. Insert a sharp pencil into the holder of the compass.

2. Open the compass to the radius desired for your circle. The radius is the distance from the center point of the circle to the outer edge.

3. Place the compass point on a piece of paper where you would like the center point of the circle to be.

4. Place the point of the pencil on the paper.

5. Rotate the compass to mark a circle on the paper with the pencil. Draw without lifting the point of the compass off the paper.

Learning Task 1. The figure at the right is a circle with center at M. Name the following:

1.        Center

2.        Four radii

3.        Diameter

4.        At least two central angles

5.        Inscribed angle

6.        Two chords

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Learning Task 3.

Write True if the statement is correct. If not, write False.

Multiple Choice

1. The diameter of the circle is twice the length of the radius.

• True

• False

Multiple Choice

2. The longest chord in a circle is the diameter.

• True

• False

Multiple Choice

3. If a radius measures 12 cm, then the measures of the diameter is 6 cm.

• True

• False

Multiple Choice

4. The length of every chord in a circle is always greater than the length of a radius.

• True

• False

Multiple Choice

5. The vertex of the central angle is the center of the circle.

• True

• False

Multiple Choice

6. The vertex of an inscribed angle is any point inside the circle.

• True

• False

Multiple Choice

7. We can draw circles with different sizes but the same center.

• True

• False

Multiple Choice

8. A line and a circle can intersect in just one point.

• True

• False

Multiple Choice

9. Every diameter intersects the circle in exactly two points.

• True

• False

Multiple Choice

10. A circle is labeled by its center point.

• True

• False

Learning Task 4. Use a compass to draw a circle of radius 4 cm. (Follow the three easy steps)

• Step 1: Use a ruler to set the distance from the point of the compass to the pencil's lead at 4 cm.

• Step 2: Place the point of the compass at the center of the circle.

• Step 3: Draw the circle by turning the compass through 360º.

   

Learning Task 5.

Identify each element.

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Great Job!