Circle Properties An Arc is a fraction of the circumference A sector is a fraction of a circle. Two radii and an arc A B O 3 cm r = 3 cm d = 6 cm Arc AB.

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Presentation transcript:

Circle Properties An Arc is a fraction of the circumference A sector is a fraction of a circle. Two radii and an arc A B O 3 cm r = 3 cm d = 6 cm Arc AB = Finding the length of an arc Arc = fraction of the circumference To get circumference need d Write down r= and d= work out values Fraction Part Total Angle in Sector 360 ° 50 ° AOB =50 ° x 3.14 x 6 dd of Arc AB = Minor Arc Major Arc An Arc goes from one point on the circumference to another. (Complete Turn)

Area of an Arc Length of Arc =Of Circumference Area of Sector =Of Area of Circle Angle at centre =Of Complete Turn To find Area of a sector Area of Sector =Of Area of Circle Area= Angle in Sector 360° x π x r x r 5 cm r = 5 Area Sector = 110° O A B AOB=110° π r² of 110° 360° x 3.14 x 5 x 5 A = A = 78.5 ÷ 360 x 110 A = …. A= 24.0 cm 3 ( 1dp )

Calculate Angle of a sector 12 cm cm² C O D COD Find Angle = of 360° Need information from sector and whole circle Know Area of Sector ……. part Can find Area of Circle ……. total Angle = of 360° x 12 x 12 π r² Angle = 360 ÷ x = …. COD = 128° ( 1dp ) for fraction

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 The dashed line is a radius. It meets the tangent a 90°. Draw tangent and radius. To solve angle problems draw the diagram a step at a time 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° a 90° 20° 70° 90° 20° 70° 36° 54° 90° 20° 70° 36° 54° 56° = 180