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An Arc goes from one point on the circumference to another. Circle Properties Minor Arc Major Arc An Arc is a fraction of the circumference A sector is a fraction of a circle. Two radii and an arc Finding the length of an arc Arc = fraction of the circumference To get circumference need d O 3 cm Write down r= and d= work out values Part Fraction Total Angle in Sector 360 ° (Complete Turn) r = 3 cm A AOB =50 ° B Arc AB = Arc AB = d = 6 cm of 50 ° 360 ° d x 3.14 x 6 Area of an Arc Length of Arc = Of Circumference Area of Sector = Area of Sector = Of Area of Circle Angle in Sector 360° r=5 of A= 110° Area = Sector 360° π r² x 3.14 x 5 x 5 A = 78.5 ÷ 360 x 110 xπxrxr B AOB=110° Of Complete Turn To find Area of a sector 110° O 5 cm Of Area of Circle Angle at centre = Area= A A = 23.986 …. A= 24.0 cm3 ( 1dp ) O Calculate Angle of a sector 12 cm D Angle = 160.8 cm² C Find of 360° Need information from sector and whole circle COD Know Area of Sector ……. part Can find Area of Circle ……. total Angle = 160.8 3.14 x 12 x 12 for fraction of 360° π r² Angle = 360 ÷ 452.16 x 160.8 = 128.025…. COD = 128° ( 1dp ) Tangent A tangent is a line which meets a circle at exactly one point. If you draw a diameter from the point of contact the angle formed is a right angle A tangent to a circle if perpendicular to the radius from its point of contact 36° 20° a To solve angle problems draw the diagram a step at a time The dashed line is a radius. It meets the tangent a 90°. Draw tangent and radius. Complete the RAT. Mark in 20° angle. Angles add to 180° Repeat for the other RAT. Extend the right hand triangle. Angles on a straight line add up to 180° 36° 20° 90° a 20° 20° 36° 90° 90° 70° 70° 54° 20° 36° 54° 90° 70 + 54 + 70° 56° = 180