The relation between the chord, the diameter, and the chord's arc?

Question

If you are given the measure of the diameter of a circle and the measure of a chord on that same circle, can you find the measure of the chord's arc?

Answer 1

yes
you can find the angle subtended by the chord which will be the same as the angle subtended by the arc
the perpendicular distance can be found by using the Pythagoras theorem
that will be the adjacent side
hypotenuse will be the radius
so the central angle 2times arc cos of the above angle
if the angle is x
length of the arc=x/360(2pir)
the radius is also known (1/2d)

Answer 2

The length of the arc is the proportional element of the circumference for the given attitude. l. a. = 2 pi r * attitude / 2 pi The chord is the bottom of the triangle shaped with the help of the radius and the intersections with the circumference. there are quite some procedures to unravel that triangle. the single which comprises my options now's lc = 2 sin(attitude / 2) * r.

Answer 3

1/2 d

Answer 4

Of course, you can. This should be intuitively clear.

We know that
arc length = radius * angle subtended by chord(radians)

radius = diameter / 2

angle = arccos[(chord^2 -2r^2)/(-2r^2)] using cosine formula for a triangle that has two sides as radii in the circle and the three side as the given chord.

Answer 5

Please go through the following link.

http://mathforum.org/dr.math/faq/formulas/faq.circle.html