Chord geometry real life example8/15/2023 Calculate the area of the circular segment between the chord joining the ends of the two radii and its corresponding arc.Ī chord of 48 cm is 7 cm from the center of a circle. Calculate the total walking area available to pedestrians visiting the park.Ī central angle of 60° is plotted on a circle with a 4 cm radius. Calculate the area of the circular trapezoid formed by the radii and concentric circles.Ī circular fountain of 5 m radius lies alone in the center of a circular park of 700 m radius. Two radii (plural for radius) OA and OB form an angle of 60° for two concentric circles with 8 and 5 cm radii. Real-life Examples of Tangent of a Circle (i) When a cycle moves along a road, then the road becomes the tangent at each point when the wheels roll on it. The entire area of the park has grass with the exception of the bases for the lamps. In a circular park with a radius of 250 m there are 7 lamps whose bases are circles with a radius of 1 m. Calculate the maximum distance travelled by the seat of the swing when the swing angle is described as the maximum.įind the area of a circular sector whose chord is the side of the square inscribed in a circle with a 4 cm radius. The rope that attaches a swing to a tree is 1.8 m long and the maximum difference between trajectories is an angle of 146°. Calculate the distance travelled by each when they have rotated 50 times around the center. Exercise 10Ĭalculate the area enclosed by the inscribed and circumscribed circles to a square with a diagonal of 8 m in length.Īnne is riding a horse which is tied to a pole with a 3.5 m piece of rope and her friend Laura is riding a donkey which is 2 m from the same center point. Exercise 9Ī chord of 48 cm is 7 cm from the center of a circle. Calculate the area of the circular segment between the chord joining the ends of the two radii and its corresponding arc. Exercise 8Ī central angle of 60° is plotted on a circle with a 4 cm radius. Figure 2 The relationship between equality of the measures of (nondiameter) chords and equality of the measures of their corresponding minor arcs. Calculate the total walking area available to pedestrians visiting the park. Example 1: Use Figure 2 to determine the following. Exercise 7Ī circular fountain of 5 m radius lies alone in the centre of a circular park of 700 m radius. Calculate the area of the circular trapezoid formed by the radii and concentric circles. Two radii (plural for radius) OA and OB form an angle of 60° for two concentric circles with 8 and 5 cm radii. In a clock, we observe that the second’s hand rapidly goes around the clock’s dial and its tip moves in a round path. Exercise 4Ĭalculate the shaded area, knowing that the side of the outer square is 6 cm and the radius of the circle is 3 cm. Chord and Arc Properties with Theorems: In our day-to-day life, we come across many objects which are round in shape, such as dials of many clocks, wheels of a vehicle, bangles, key-rings etc. Exercise 3įind the area of a circular sector whose chord is the side of the square inscribed in a circle with a 4 cm radius. Calculate the maximum distance travelled by the seat of the swing when the swing angle is described as the maximum. Calculate the distance travelled by each when they have rotated 50 times around the centre. You may assume that A is the center of the circle.Anne is riding a horse which is tied to a pole with a 3.5 m piece of rope and her friend Laura is riding a donkey which is 2 m from the same center point. Some concentric circle examples have been provided below: Concentric Circle Equations We know that the equation of circle with centre (-g, -f) and radius g 2 +f 2 -c is x2 + y2 + 2gx + 2fy + c 0. In problems 25-27, what can you conclude about the picture? State a theorem that justifies your answer. There are a lot of real-life concentric circle examples therefore you don’t have to imagine them. Round your answer to the nearest tenth of a degree.
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