Post on 07-Jan-2016
description
@lhmaths: Lesley Hall
Circle Theorems: 1. The angle subtended at the centre of a circle is twice the angle subtended at the circumference.
AB
angle subtended at the centre
@lhmaths: Lesley Hall
Circle Theorems: 1. The angle subtended at the centre of a circle is twice the angle subtended at the circumference.
AB
angle subtended at the circumference
C
@lhmaths: Lesley Hall
Circle Theorems: 1. The angle subtended at the centre of a circle is twice the angle subtended at the circumference.
AB
C
angle at the centre is twice that at the circumference
@lhmaths: Lesley Hall
Circle Theorems: 1. The angle subtended at the centre of a circle is twice the angle subtended at the circumference.
AB
C
angle at the centre is twice that at the circumference
x
2x AOB = 2 x ACB
O
@lhmaths: Lesley Hall
Circle Theorems: 2. Angles subtended by an arc in the same segment of a circle are equal.
AB
C
x
2x
Given: The angle subtended at the centre of a circle is twice the angle subtended at the circumference.
@lhmaths: Lesley Hall
Circle Theorems: 2. Angles subtended by an arc in the same segment of a circle are equal.
AB
C
x
2x
D
xx
E
@lhmaths: Lesley Hall
Circle Theorems: 2. Angles subtended by an arc in the same segment of a circle are equal.
AB
C
x
2x
D
xx
E ADB = ACB = AEB
@lhmaths: Lesley Hall
Circle Theorems: 2. Angles subtended by an arc in the same segment of a circle are equal.
AB
C
xD
xx
E
AB
C
DE
ADB = ACB = AEB
@lhmaths: Lesley Hall
Circle Theorems: 2. Angles subtended by an arc in the same segment of a circle are equal.
AB
C
DE
AB
arc AB
angle subtended by arc ABangles subtended by arc AB
ADB = ACB = AEB
@lhmaths: Lesley Hall
Circle Theorems: 2. Angles subtended by an arc in the same segment of a circle are equal.
AB
C
DE
angle subtended by arc ABangles subtended by arc AB
in the same segment
ADB = ACB = AEB
@lhmaths: Lesley Hall
Circle Theorems: 2. Angles subtended by an arc in the same segment of a circle are equal.
AB
C
DE
Angles subtended by arc AB
in the same segment
ADB = ACB = AEB
are equal.
@lhmaths: Lesley Hall
Circle Theorems: 1 & 2 ExamplesObjective: To use theorems 1
and 2 to calculate angles.
500
y400
960
z x500 x = y = 180 – (96 +
50) = 180 – 146
= 340