Thread: Circle Theory

How do I actually identify if 2 angles are in the same segment?

Originally Posted by Punch

How do I actually identify if 2 angles are in the same segment?

hi Punch,

in the circle, origin (0,0), unit radius,

Sin(angle) is the vertical co-ordinate,
Cos(angle) is the horizontal co-ordinate of a point on the circumference.

Hence if the "sign" (positive or negative) of sin(angle) is the same for both angles
and the "sign" of cos(angle) is the same for both angles,
then the angles are in the same quadrant.

There are other ways of course.
Did you have a specific situation?

Yes I have a situation... I don't understand why CEB is not equals to CAB. Aren't they angles in the same segment since they are from the same arc?

Hi Punch,

yes, that's an error,

since triangle BCE is isosceles, then angle BCA is 55 degrees.
Then, angles CBE, BCE and BEC sum to 180 degrees, so angle BEC is 180-150=30 degrees.

Hence, angle CAB is also 30 degrees.

Angle ABE should be 20 degrees.

Oh My goodness this was one of the o'levels question...