Angle at the Centre of a Circle Proof
Here we want to prove that the angle ACB is double angle ADB
ACB = 2(ADB)
ACB = 2(ADB)
First: Join point D to point C and extend on to Radius to create point X
To prove: Angle ACB = 2 Angle ADB
Proof:
Similarly Angle BCX = 2 Angle CDB
Angle ACX + Angle BCX = 2 Angle CDA + 2 Angle CDB
Therefore: Angle ACB = 2 Angle ADB
To prove: Angle ACB = 2 Angle ADB
Proof:
- AC = CB because they are the same radius.
- Angle CAB = Angle CBD because it is an isosceles triangle.
- Angle ACX = Angle DAC and angle CDA because 2 opposite interior angles are equal to the exterior angle of a triangle.
- Angle ACX =Angle CDA and Angle CDA
- Therefore Angle ACX = 2 Angle CDA
Similarly Angle BCX = 2 Angle CDB
Angle ACX + Angle BCX = 2 Angle CDA + 2 Angle CDB
Therefore: Angle ACB = 2 Angle ADB
Interactive of Proof