If central angle θ cuts off a chord of length c in a circle of radius r , then the relationship between θ , c , and r is given by Find θ , if c = r
A)θ = 120°
B)θ = 90 °
C)θ = 20 °
D)θ = 180 °
E)θ = 120 °

Question

If central angle θ  cuts off a chord of length c  in a circle of radius r , then the relationship between θ , c , and r  is given by   Find θ , if ​c ​ =  ​r ​ 
A)​θ = 120° 
B)​θ = 90 ° 
C)​θ = 20 ° 
D)​θ = 180 ° 
E)​θ = 120 °

Quizplus · Accepted Answer

According to the formula given, sin(θ/2) = c/2r. If c = r, then sin(θ/2) = 1/2. Solving for θ gives θ = 2sin⁻¹(1/2), which is equal to 120°. Therefore, the best choice is A.

If Central Angle θ Cuts Off a Chord of Length