# A circle has a center at #(7 ,9 )# and passes through #(1 ,3 )#. What is the length of an arc covering #(3pi ) /4 # radians on the circle?

Use the circle standard form

By signing up, you agree to our Terms of Service and Privacy Policy

To find the length of an arc covering ( \frac{3\pi}{4} ) radians on the circle, we first need to find the radius of the circle. The distance between the center of the circle (7, 9) and the point on the circle (1, 3) is the radius.

Using the distance formula: [ \text{radius} = \sqrt{(7 - 1)^2 + (9 - 3)^2} = \sqrt{6^2 + 6^2} = \sqrt{36 + 36} = \sqrt{72} = 6\sqrt{2} ]

The circumference of the circle is ( 2\pi r ), where ( r ) is the radius. [ \text{circumference} = 2\pi \times 6\sqrt{2} = 12\pi\sqrt{2} ]

To find the length of the arc for ( \frac{3\pi}{4} ) radians, we use the formula ( \text{arc length} = \text{radius} \times \text{angle in radians} ). [ \text{arc length} = 6\sqrt{2} \times \frac{3\pi}{4} = \frac{18\pi\sqrt{2}}{4} = \frac{9\pi\sqrt{2}}{2} ]

So, the length of the arc covering ( \frac{3\pi}{4} ) radians on the circle is ( \frac{9\pi\sqrt{2}}{2} ).

By signing up, you agree to our Terms of Service and Privacy Policy

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- A triangle has vertices A, B, and C. Vertex A has an angle of #pi/2 #, vertex B has an angle of #( pi)/4 #, and the triangle's area is #12 #. What is the area of the triangle's incircle?
- Two circles have the following equations #(x +5 )^2+(y -2 )^2= 36 # and #(x -1 )^2+(y -1 )^2= 81 #. Does one circle contain the other? If not, what is the greatest possible distance between a point on one circle and another point on the other?
- A triangle has corners at #(7 , 9 )#, #(3 ,7 )#, and #(1 ,8 )#. What is the radius of the triangle's inscribed circle?
- A circle has a center that falls on the line #y = 2/3x +7 # and passes through #(5 ,7 )# and #(3 ,2 )#. What is the equation of the circle?
- A triangle has sides with lengths of 3, 7, and 2. What is the radius of the triangles inscribed circle?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7