### XY is a chord of a circle of radius 5cm, subtending an angle of 50°...

XY is a chord of a circle of radius 5cm, subtending an angle of 50° at the centre. Find
(a) the length of the chord XY.
(b) the length of the arc XY correct to 3 sign. Figures
(c) proof that XY is the chord of the circle?

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(I) y= ?
Length of a chord= 2rsin(θ/2)

θ= 50° and r= 5cm

y= 2(5)(sin 25°)= 10sin25°= 4.23cm

(II) z= ?
Length of an arc= (θ/360)2πr

z= (50/360)2(π)(5)= 4.36cm in 3 s.f.

(III) A chord is that line in a circle that runs from one point of a circumference to the other without passing the centre. XY, which is a line, follows this definition.
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I cannot upload an image now but I'll try to be as explanatory as possible

first draw a circle and outline its radius and then its chord

secondly draw a perpendicular bisector of the angle subtended by the cord so the angle refuces to 25°

sin 25°=x/5
where x is half the cord lenght
x=,5*Sin(25)=10+33*1/60+55.64*1/3600
=~2.11cm

•^•chord length=2*ans=Rationalize(4.2261826174)cm
~4.23cm

2) Length of the arc =

2πr /360

=Rationalize(4.36332313)
~4.36cm

3) the simple proof is that since the length of XY is not up i.e < to the length of the diameter=2r=10cm it is definitely a chord
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• Melo: Eddy you try but not correct.
1 week ago