P1 length of a chordWatch

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#1
is there a formula for working this out?
0
14 years ago
#2
yes, the cosine rule.

a^2 = b^2 + c^2 - 2bc(cosA)

in terms of a circle, a will be the chord length, and b and c are both the radius. theta is the angle from the centre.

a^2 = r^2 + r^2 - 2r*r(cos theta)
a^2 = 2r^2 - 2r^2(cos theta)
a^2 = 2r^2(1 - cos theta)

from this you can tell that as the LHS is a perfect square, the RHS must be positive and have either two negativ or two positive factors. as one factor is 2r^2, always positive, (1- cos theta) must also be positive, meaning cos theta must be smaller than 1, meaning theta must be in the range 0<theta<pi, which makes sense really.

just some additional maths there :-p
0
14 years ago
#3
Depends what information you are given. Draw a diagram and go from there.
0
14 years ago
#4
(Original post by mik1a)
a^2 = 2r^2(1 - cos theta)
If you apply the cos(2x) formula you get

a = 2 r cos(theta/2)

which is easier to remember, and sort of more obvious if you picture the diagram and do a bit of trig.
0
14 years ago
#5

Use distance formula:

(chord)^2= (X1 - X2) + (Y1 - Y2)

Remember to square root. A bit like Pythagarus but but chord is hypothesis and end point of chord (Xs and Ys) are what u put in.

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