Thread: Points on a circle.1

1. Points on a circle.1

In the diagram, a is the center of the circle, A,b and C are points on the circle.

Angle COA = 130
i) Find the size of angle CBA

I know it's 65 because it's half of CaA (O doesn't work in paint) but what is this law called? What is the CaA angle called and the CBA angle called?

This is all GCSE standard, please do not venture further. P.S that angle reads '230'

2. Originally Posted by Mukilab In the diagram, a is the center of the circle, A,b and C are points on the circle.

Angle COA = 130
i) Find the size of angle CBA

I know it's 65 because it's half of CaA (O doesn't work in paint) but what is this law called? What is the CaA angle called and the CBA angle called?

This is all GCSE standard, please do not venture further. P.S that angle reads '230'

Definition: 1) An inscribed angle is one whose vertex is on the circle and whose legs intersect the circle
2) A central angle is one whose vertex is at the circle's center and whose legs intersect the circle

Theorem: An inscribed angle's value is exactly half the central angle when they both subtend the same arc.

Tonio

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