Circle Geometry

Well where should I start. In class we were given our first assignment in class, it wasn't hard but it was relatively new to some of us. Investigation 1 and 2 were our given assignments and here are completed ones in case anyone didn't quite get it .

INVESTIGATION 1
A- Construct 4 different chords (a straight line joining two points on the circumference of a circle), AB ,CD, EF, and GH

• But none of them should be diameters (longest possible chord in a circle that passes through the center) nor should they be parallel. The 4 different chords are in black
  

B- O is the center of the circle. Construct lines from the center that are perpendicular to each of the chords. AB, CD, EF and GH. Label the new points where the new lines meets W, X, Y and Z , The perpendicular lines will be in red . The perpendicular lines are also known as bisectors, because they cut the chord into two.

C- Measure the lengths of the AW and BW. Do so with the rest so every chord has two measurements on either side of the perpendicular line

D- Now after your picture is drawn you should see a relationship between a chord and their perpendicular line.

A LITTLE HELP: "A line perpendicular to a chord, that passes through the center of a circle, the chord."

Here is an example of what your drawing should somewhat look like

INVESTIGATION 2
A- Like the A in Investigation 1 construct 4 different chords AB, CD, EF and GH

• Remember none of them should be parallel to each other nor be diameters
  

B- Construct perpendicular bisectors for each chord. Each bisector should be a chord.

KEY: the way to find the bisector is to measure the chord, and find the midpoint. At that midpoint line up a triangle from your geometry set to make a 90 degree angle and draw the perpendicular.

C- What do all the bisectors have in common? Well once your done they should all intersect at the same point.
D- What can you say about any perpendicular? You could say that the perpendicular bisector of any chord will always dissect the center of the circle.

This diagram should give you an idea of how it should look


Example: chord AB. Length of chord divided by two = point where bisector should cross

To complement our learning we also learned some definitions to go along with our new unit
Bisect- to cut into two exact equal halves
Subtend(subtended)- to hold arms of an angle open by an arc

Well that's it thats all folks
Oh yea before I forget

Share the kindness and leave some kind comments on our friends blog in Scotland
If you forgot the address its exc-el.org.uk/blogs/s3srcibeposts, I checked it out and its pretty neat!


Ex 30 for homework.
NEXT will be ......................Crysta!