A chord of a circle is subtended by an angle of x degrees. The radius of the circle is 6 √ 2. What is the length of the minor arc subtended by the chord?

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Presentation transcript:

A chord of a circle is subtended by an angle of x degrees. The radius of the circle is 6 √ 2. What is the length of the minor arc subtended by the chord? We can work this out without a calculator. We can because we know about surds.

A chord of a circle is the hypotenuse of an isosceles right triangle whose legs are the radii of the circle. The radius of the circle is 6 √ 2. What is the length of the chord and the minor arc subtended by the chord? Find the chord using Pythagoras and surds and do not evaluate your answer.

A chord of a circle is the hypotenuse of an isosceles right triangle whose legs are the radii of the circle. The radius of the circle is 6 √ 2. What is the length of the chord? (6 √ 2) 2 + (6 √ 2) 2 = chord 2 (36 x 2) + (36 x 2) = chord 2 Chord = √ 144= 12

A chord of a circle is the hypotenuse of an isosceles right triangle whose legs are the radii of the circle. The radius of the circle is 6 √ 2. What is the length of the minor arc subtended by the chord? Find Circumference using surds and keep your answer in terms of π

A chord of a circle is the hypotenuse of an isosceles right triangle whose legs are the radii of the circle. The radius of the circle is 6 √ 2. What is the length of the minor arc subtended by the chord? Circumference = πD C = 2x6 √ 2 π C = 12 √ 2 π

A chord of a circle is the hypotenuse of an isosceles right triangle whose legs are the radii of the circle. The radius of the circle is 6 √ 2. What is the length of the minor arc subtended by the chord? C = 12 √ 2 π Minor arc =  x12 √ 2 π Minor arc = 3 √ 2 π

A chord of a circle is the side of an equilateral triangle and equal to the radius of the circle. The radius of the circle is 6 √ 2. What is the length of the minor arc subtended by the chord? Remember C = 12 √ 2 π

A chord of a circle is the side of an equilateral triangle and equal to the radius of the circle. The radius of the circle is 6 √ 2. What is the length of the minor arc subtended by the chord? C = 12 √ 2 π Chord =  x 12 √ 2 π Chord = 2 √ 2 π

A chord of a circle is subtended by an angle of x degrees. The radius of the circle is 6 √ 2. What is the length of the minor arc subtended by the chord? Remember C = 12 √ 2 π

A chord of a circle is subtended by an angle of x degrees. The radius of the circle is 6 √ 2. What is the length of the minor arc subtended by the chord? C = 12 √ 2 π Chord = x/360 X 12 √ 2 π Chord = x/30 √ 2 π Chord = x √ 2 π/30

Note Sometimes it is actually easier to work with surds! Do not be in a rush to evaluate π