The subtending arc
Part I
Below is a circle of centre O. Points A, B and C are points on the circle.
α is the angle at the centre and θ is an angle on the circle. Both angles are subtended by the
same arc LM.
1.
Using a protractor, measure the angles α and θ.
2.
What is the relation between angles α and θ?
3.
Draw [AL], [AM], [CL] and [CM].
4.
Measure the angles LAM and LCM .
5.
What is the relation between the angles above and α?
6.
Generalize a statement describing the relation between the angle at the centre and the
angles on the circle subtended by the same arc.
Part II
1.
Will your general statement above be valid in the two cases below? Explain your
answer.
Circle of centre O and AB diameter
2.
Circle of centre K.
Prove the general statement you reached in Part I in the following case.