A circle has a center at $(1, 3)$ $(1 ,3 )$ and passes through $(2, 4)$ $(2 ,4 )$ . What is the length of an arc covering $π$ $pi$ radians on the circle?

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A circle has a center at $(1, 3)$ $(1 ,3 )$ and passes through $(2, 4)$ $(2 ,4 )$ . What is the length of an arc covering $π$ $pi$ radians on the circle?

1 Answer

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Answer 1 · 2016-02-06T13:19:57

$4.44$ $4.44$ units

Explanation:

The radius of the circle is the distance between the centre and the given point.

$r = d ((1, 3); (2, 4)) = \sqrt{{(2 - 1)}^{2} + {(4 - 3)}^{2}} = \sqrt{2}$ $r=d((1,3);(2,4))=sqrt((2-1)^2+(4-3)^2)=sqrt2$

So the equation of this circle is ${(x - 1)}^{2} + {(y - 3)}^{2} = 2$ $(x-1)^2+(y-3)^2=2$ .

An arc length covering $π$ $pi$ radians ( $180^{\circ}$ $180^@$ ) is effectively half the circumference of the circle, ie
$\frac{1}{2} \times 2 π r$ $1/2xx2pir$

$= \frac{1}{2} \times 2 \times π \times \sqrt{2}$ $=1/2xx2xxpixxsqrt2$

$= π \sqrt{2}$ $=pisqrt2$ units

$= 4.44$ $=4.44$ units.

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A circle has a center at $(1, 3)$ $(1 ,3 )$ and passes through $(2, 4)$ $(2 ,4 )$ . What is the length of an arc covering $π$ $pi$ radians on the circle?

1 Answer

Explanation:

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Impact of this question

Science

Math

Humanities

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A circle has a center at (1,3)(1 ,3 ) and passes through (2,4)(2 ,4 ). What is the length of an arc covering πpi radians on the circle?

1 Answer

Explanation:

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Impact of this question

A circle has a center at $(1, 3)$ $(1 ,3 )$ and passes through $(2, 4)$ $(2 ,4 )$ . What is the length of an arc covering $π$ $pi$ radians on the circle?