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dexar [7]
3 years ago
11

A circle is shown. 2 raddi are drawn. A chord connects the points of the radii on the circle to each other to form a triangle. T

he radii have lengths of 5 feet. A perpendicular bisector cuts through an angle with a measure of 72 degrees and cuts the opposite side of the triangle into 2 equals parts with measures of 2.9 feet. The length of the bisector is 4 feet. The space between the chord and the outline of the circle is shaded. What is the area of the shaded portion of the circle? (5π – 11.6) ft2 (5π – 5.8) ft2 (25π – 11.6) ft2 (25π – 5.8) ft2
Mathematics
1 answer:
iragen [17]3 years ago
3 0

Answer:

(5\pi-11.6)ft^2

Step-by-step explanation:

Given:

Length of radius of circle = 5 feets

Length of perpendicular bisector = 4 feets

To find:

Area of the shaded portion of the circle

Solution:

As OD is perpendicular bisector of AB,

AB=2AD=2(2.9)=5.8\,\,feets

\angle ODA=90^{\circ}

Area of \Delta AOB = 1/2 (base) × (height) = \frac{1}{2}\times 4\times 5.8=11.6  square feets

Area of sector AOBC = \frac{\angle AOB}{360^{\circ}}\pi(r^2)=\frac{72^{\circ}}{360^{\circ}}\pi(5^2)=5\pi  square feets

Here, r denotes radius of circle

So,

Area of shaded portion = Area of sector AOBC - Area of \Delta AOB = (5\pi-11.6)ft^2  

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