Create a diagram of part of a circle with a whole chord shown on it, and create a part of a line segment that would be a diameter if extended.
The key idea here, is that when you see a part of a segment that is perpendicular to a chord, and bisecting the chord, that segment must be a diameter.
If it’s just perpendicular, or just a bisector, that is not enough. It must be both for us to be absolutely sure that it’s a diameter.
Adding and Subtracting Areas
If you know all of the areas of the parts of a figure, then you can add them all up to get the area of the total, as long as none of the parts overlap.
In the diagram above, you can find the two sides of the rectangle (5 and 9) to get the area of 5•9=45 square units, or you can add all of the separate areas: 2+4+3+8+16+12=45 square units.
If any parts overlap, you need to subtract off the area of the overlap to get the correct total.
Find the area of the figure above.
Notice that in this case, the square and the circle overlap. So we will find the areas of the whole square, the whole circle, and then find the area of the part that overlaps, and subtract that from adding the square and circle areas to get our answer.
Also notice that the overlap area is a sector area (1/4 of the circle area)
Area of the circle= π•5^2=25π=78.5
Area of the square=5•5=25
Area of overlap (sector area)=1/4•78.5=19.6
Area of figure= 78.5+25-19.6=83.9
Segments on Circles
A chord is a segment on a circle connecting two points on the circle.
A diameter is a chord that goes through the center.
(Key idea here, is reminding you that a diameter is a type of chord, so things that work for chords, work for diameters!)
Recall: Chord-Chord Property- a•b=c•d, where a and b are two parts of one chord, and c and d are two parts of the other chord.
Below is the worksheet that we worked on in class: