Math Is Fun Forum

Stanley

Member

Registered: 2006-10-27

Posts: 9

Area of the circle!?

How to find the area of the smallest piece of the remaining circle, that is cut by a chord?

The maximum distance between the line segment (that makes right angle) from the line to end of the circle edges is considered height which is known together with the radius of the circle.

Regards,
Stanley

Devantè

Real Member

Registered: 2006-07-14

Posts: 6,400

Re: Area of the circle!?

This doesn't belong in the formula section, this should be in the Help Me section.

justlookingforthemoment

Moderator

Registered: 2005-05-26

Posts: 2,161

Re: Area of the circle!?

Topic moved to 'Help Me!'

luca-deltodesco

Member

Registered: 2006-05-05

Posts: 1,470

Re: Area of the circle!?

do you mean height is the distance from centre of circle along a perpendicular to the chord?

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Stanley

Member

Registered: 2006-10-27

Posts: 9

Re: Area of the circle!?

Yes Luca, that must be right, even the perpendicular line will start from the center of the chord inorder to have the maximum distance.

Regards,
Stanley

luca-deltodesco

Member

Registered: 2006-05-05

Posts: 1,470

Re: Area of the circle!?

ok well then think of it like this: (little drawing in pics)

the area A can be found by finding the area of the sector defined by the angle on either side minus the area of the triangle formed with the chord.

to find the angle, you would have

the area of the whole sector would be

for the area of triangle, we first need the length of the chord, this will be equal to

so the area of triangle underneath chord

the area A will then be.

Last edited by luca-deltodesco (2006-10-30 08:53:40)

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The Beginning Of All Things To End.
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Stanley

Member

Registered: 2006-10-27

Posts: 9

Re: Area of the circle!?

Excellent!

Thanks,
Stanley