An arc which subtends and angle of 60° at O is shown below. Find the ratio of r : R.
Select the correct answer from the following choices.
i) 1 : 2
ii) 1 : √2
iii) 1 : √3
iv) 1 : 3
With reference to the following diagram;
The radius ABO passed through the center of the circle ARC and bisects the angle EOD.
Triangle BCO is a right angled triangle with angles 30°, 60° and 90°.
if BC = r, then BO = 2r.
Therefore radius of the arc DAE = AB + BO = 3r
Given that the radius of the arc DAE = R,
That is, R = 3r
Therefore the ratio of r : R is 1 : 3.
The answer is (iv).
- Hey Math! assignment (E-Maths), July 2010, Question #7, Circle and trigonometry