Chord in mathematics, technical drawing and some other industries of knowledge it is accepted to call a straight line piece which connects two any points of a circle. The longest chord passing through the center of a circle is called diameter.
It is required to you
- - circle radius:
- - chord arch length;
- - chord arch corner;
- - paper and drawing tools.
Instruction
1. Execute the drawing according to statements of the problem. Draw a circle of the set radius. If the corner of an arch which pulls together chord, construct it is known to you. Carry out radius, postpone the necessary corner by means of a protractor and carry out one more. Connect points of intersection of radiuses to a circle a straight line. It will also be a chord necessary to you. If the corner is unknown, draw any chord.
2. Execute additional construction. Halve a chord and carry out to this point a perpendicular from the center of a circle. At you the isosceles triangle which height is the perpendicular to the middle of a chord turned out.
3. Designate the radius as R, a chord - as h, and the central corner - as it is fashionable to h to find A. Togd or through a sine And, or through a cosine. In the first case the formula will look as h=2R*sinA/2 where R is the known radius of a circle. In the second case the formula will look as h=R * √ (1-cosB).
4. One of the most ancient geometrical tasks - to find chord length if the radius of a circle and length of an arch are known. Calculate length P circle. It is equal to the doubled radius increased by coefficient P it is possible to Express it a formula P=2PR.
5. Calculate the relation of the set l arch length to P circle length. Thus you calculate the arch corner size. In this case it is unimportant, there will be it in degrees or radians. Knowing its size, calculate a sine of a half corner. After that you can calculate the chord size on a formula already known to you.
6. Quite often it is necessary to face also an opposite task - for example, to find arch length on the radius of a circle and length of a chord. Using the theorem of sine, calculate the size of a half, and then and whole central corner. Knowing it, based on the ratio of arch length to length of a circle calculate the arch length unknown to you.