Topics covered within this unit: 29.1 Revision of Circles 1 29.2 Angles in a semicircle 29.3 Cyclic quadrilaterals
The Learning Outcomes covered in this unit are contained in the following sections:
GT.1 GT.2c GT.3c GT.3b GT.3d GT.3e
Key words
Standing on the arc Cyclic quadrilateral
29.1 Revision of Circles 1
By the end of this section you should: ● be able to fi nd the area and perimeter of shapes involving circles
Circles 2
Something to think about …
The theorems of circle geometry are not obvious to us a lot of the time. In fact, most people are quite surprised by the results when they fi rst see them. One such theorem is attributed to Thales of Miletus (c. 620–546 BCE) and involves angles in a circle.
A taco shell is in the shape of a semicircle.
Find the measure of ∠EFG, ∠FEG and ∠FGE in the taco shown without using a protractor, given that |EF| = |FG|.
E F G D
We learned about circles in Section B, Unit 16. Radius Radius
Circle
π is a constant value for all circles. π = circumference of a circle
__________________ diameter of the circle
Disc
Area = πr2 Circumference (length) = 2 πr
These formulae appear in the formulae and tables booklet.
π does not have an exact value, but when doing calculations, we can use the approximate values 3·14 or 22 on the calculator.