Question

The diameter of circle C is 18 cm. Chord AD is the same length as a radius. Use this information, the diagram, and your experiences in geometry this semester to answer these questions. a) what are the measures of the angles BDA and DBA?. b) What is the sine of angle DBA? c) Find the length of arc AB to the nearest hundredth. d) How does the length of arc AD compare to the length of arc AB? e) If FE = 1/2 BD, then what is the degree measure of arc EF?

Answer 1

A ) ∠ BDA = 60°
∠DBA = 30°
B ) sin (∠DBA ) = sin 30° = 1/2
C ) arc AB = 1/3 · 2 r π = 1/3 · 18 π = 6 π = 6 · 3.14 = 18.84 cm
D ) arc AD : arc AB = 1 : 2
E ) Degree measure of an arc is equal to the measure of the central angle that intercepts the arc. The degree measure is 60° ( F E = 9 cm, r = 9 cm ).