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# In the figure, a, b, c, d, e, f, g, h, i, and j are chords of the circ

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Math Expert
Joined: 02 Sep 2009
Posts: 53066
In the figure, a, b, c, d, e, f, g, h, i, and j are chords of the circ  [#permalink]

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09 Oct 2018, 22:28
00:00

Difficulty:

65% (hard)

Question Stats:

44% (02:03) correct 56% (01:41) wrong based on 57 sessions

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In the figure, a, b, c, d, e, f, g, h, i, and j are chords of the circle. Which two chords are parallel to each other?

(A) a and f
(B) b and g
(C) c and h
(D) d and i
(E) e and j

Attachment:

circle.jpg [ 55.23 KiB | Viewed 539 times ]

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Re: In the figure, a, b, c, d, e, f, g, h, i, and j are chords of the circ  [#permalink]

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09 Oct 2018, 22:35
Chords e and j are parallel to each other & Option (E) is correct.

For two chords to be parallel they need to have 180 degree separation in alignment. The figure gives us the difference between two chords, so we must find the correct chords between whom a total of 180 deg separation is present.

Chord e + ( 40 + 35 + 35 + 40 + 30 ) = Chord J. In the anticlockwise direction

Chord e + 180 deg = Chord j.

Hence they are parallel and Option (E) is our choice.

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Re: In the figure, a, b, c, d, e, f, g, h, i, and j are chords of the circ  [#permalink]

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10 Oct 2018, 02:42
chetan2u sorry to bug again but your approach

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Re: In the figure, a, b, c, d, e, f, g, h, i, and j are chords of the circ  [#permalink]

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10 Oct 2018, 21:35
Any quicker way to do this .
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Re: In the figure, a, b, c, d, e, f, g, h, i, and j are chords of the circ  [#permalink]

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11 Oct 2018, 01:55
Bunuel wrote:

In the figure, a, b, c, d, e, f, g, h, i, and j are chords of the circle. Which two chords are parallel to each other?

(A) a and f
(B) b and g
(C) c and h
(D) d and i
(E) e and j

Attachment:
circle.jpg

When I see this figure, I don't see circles and chords - I see a polygon. Had it been about circles and chords, there would have been 1 or 2 chords. These all are making a complete polygon inscribed in the circle.
We are given exterior angles of a polygon. I know that the sum of all exterior angles will be 360.
Consider the side a. It is turned 40 degrees to get side b. Side b is turned 35 degrees to get side c and so on...
When are 2 lines parallel? When a side is eventually turned 180 degrees, it will have the same slope as before.

I notice the figures 32, 32 and 36. They are different from the rest which end in a 5 or a 0. I am thinking that if one of them is a part of my sum of 180, all 3 need to be so add up to 100. Fortunately I have a 45 degrees angle between them and a 35 degrees angle after them.
This tells me that side e is turned 180 degrees clockwise to get side j (32 + 36 + 45 + 32 + 35)

So sides e and j are parallel

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Re: In the figure, a, b, c, d, e, f, g, h, i, and j are chords of the circ   [#permalink] 11 Oct 2018, 01:55
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