Question

A, C, and D are point on a circle of a radiu 4cm, centre O.

BA and BC are tangent to the circle.
OB = 10cm
Work out the length of arc ADC.

Answer 1

Explanation:

OB = 10 cm

OA = OC = Radius = 4 cm

COS <AB = OA/OB = 4/10 = 2/5 =

COS< COB = OC/OB = 4/10 = 2/5

=> <AOC = <AOB + <COB

=> <AOC = Cos-¹(2/5) + Cos-¹(2/5)

=> <AOC = 2 Cos-¹(2/5)

=> <AOC = 2 * 66.42

=> <AOC = 132.84°

if D is in minor arc then length of arc ADC. = ( 132.84°/360°) 2π = 9.274 cm

if D is in major arc then length of arc ADC. = ((360° -132.84°)/360°) 2π = 15.859 cm