Math Multiple Choice
In the figure above, AD is a diameter of the circle with center O and AO = 5. What is the length of arc BCD ?
- (A)
- (B)
- (C)
- (D)
CORRECT ANSWER - (E)
Explanation:
To solve this problem, it is helpful to draw segment OB in the figure. Since OB and OD are both radii of
the circle, they both equal 5. Therefore, the angles opposite these congruent sides of 
BOD are congruent
and 
OBD = 36°. The third angle of the triangle, BOD, equals
180°- 36°- 36° = 108°. Arc BCD is a fraction of the circumference of the circle and more specifically equals 
, which equals The correct answer is choice (D).