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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. |
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Answer» 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. 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 Learn more: Which has greater degree measure : an arc of length 5cm of circle of ... Measure of an arc of a sector of a circle is 90° and its radius is 7cm ... in the given figure, 'O' is the centre of the circle and the length of arc ... |
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