Everything Maths Grade 12

9.2 CHAPTER 9. GEOMETRY

�

A � B

O

P

ar

c

chord

tangent

diameter

radius

segment

Figure 9.1: Parts of a circle

B C

A

Figure 9.2: A right-angled triangle

1. The Theorem of Pythagoras, which states that the square on the hypotenuse of a right-angled
   triangle is equal to thesum of the squares on the other two sides. In�ABC, this means that
   (AB)^2 + (BC)^2 = (AC)^2


2. A tangent is perpendicular to the radius, drawn at the point of contactwith the circle.

Theorems of the Geometry of Circles EMCBX

A theorem is a general proposition that is not self-evident but is proved by reasoning (these proofs need
not be learned for examination purposes).

Theorem 1. The line drawn from the centre of a circle, perpendicular to a chord, bisects the chord.