Home » Questions » Unexperienced [ Ask a new question ]

IN THE FIGURE , O IS THE CENTER OF THE CIRCLE AND SEGMENT BC IS CONGRUENT TO SEGMENT OA FIND FIND EACH MEASURE

IN THE FIGURE , O IS THE CENTER OF THE CIRCLE AND SEGMENT BC IS CONGRUENT TO SEGMENT OA FIND FIND EACH MEASURE

Asked by: Guest | Views: 69
Total answers/comments: 1
Guest [Entry]

"If segments BC and OA are congruent, then segments BC and OB are also congruent since OA and OB are radii.  The radii of a circle have equal lengths.

Therefore, BC ≅ OA ≅ OB  and these segments form an equilateral isosceles triangle with 60°-60°-60° angles.

The following are measures derived from statements above:

m∠BOC = 60°  (Central angle)

m∠BOC and m∠COA are supplementary.

m∠COA = 120°

Half circle = 180°

1) arc BC = 60°

Proof: The measure of central angle and its intercepted arc are congruent.

2) arc BDA = 180°

Proof: Half circle = 360°/2  or  180°

3) arc BAC = 300°

Proof:

arc BAC = 360° - arc BC  ⇒  arc BAC = 360° -60° = 300°

4) arc AC = 120°

Proof:

arc AC = 180° - arc BC   ⇒  arc AC = 180° - 60° = 120°

5) arc CBA = 240°

Proof:

arc CBA = 360° - arc AC    ⇒   arc CBA = 360° - 120° = 240°"