A,C and D are points on a circle of radius 4cm, centre O. BA and BC are tangents to the circle. OB = 10cm. Work out the length of arc ADC. Give your answer correct to 3 significant figures.
Answers
Given : A,C and D are points on a circle of radius 4cm, centre O. BA and BC are tangents to the circle. OB = 10cm.
To find : length of arc ADC
Solution:
OB = 10 cm
OA = OC = Radius = 4 cm
Cos∠AOB = 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 (4)
= 9.274 cm
if D is in major arc then
length of arc ADC. = ( (360° -132.84°)/360°) 2π (4)
= 15.859 cm
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Answer:
15.9cm
Step-by-step explanation:
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