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8 votes
A, B and C are three points on a circle.

The radii from A, B and C are shown.
B
X
2(2x + 20°)
5x + 40°
с
Is AC a diameter of the circle?
You must show your working.

A, B and C are three points on a circle. The radii from A, B and C are shown. B X-example-1

2 Answers

5 votes

You should add 5x+40 to 2(2x+20) and x, to see if they come up to 360. If they do, AC is a diamater of the circle.

So, let’s begin.

5x+40 + 2(2x+20) + x = 360

We need to take care of the brackets first.

5x+40 + 4x+40 + x = 360

Now, we will group the parts of the equation. We will put the unknown parts on the left, and the known ones on the right.

5x + 4x + x = 360 - 40 - 40

From here on it’s pretty straight-forward.

10x= 280

Divide both sides by 10.

x=28

Moving on,

5x+40 + 2(2x + 20) + x = 360

5*28 + 40 + 2(2*28 + 20) + 28 = 360

140 + 40 + 2(56 + 20) + 280 = 360

180 + 112 + 40 + 28 = 360

360 = 360

They are equal, therefore AC is a diamater of the circle.

User Eritrean
by
5.9k points
4 votes
Yes. AC is diameter
5x +40+x+2(2x+20)=360
5x+40+x+4x+40=360
5x+x+4x+40+40=360
10x+80=360
10x=360-80
10x=280
X=280/10=28

5x+40=5*28+40
=140+40=180
So it’s diameter
User YuriyP
by
5.5k points