A problem by Er Abhishek Gupta

Level pending

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 and f c and h e and j b and g

Er Abhishek Gupta by Er Abhishek Gupta , 29, India

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4 solutions

add up all the angles in between and if it gives 180, they're parallel, such is the case with E and J

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Er Abhishek Gupta
Oct 30, 2014

Two lines are parallel to each other when the angle swept between them is 180°. Use this property to determine the answer:

Angle swept between lines e and j equals Angle between e and f + Angle between f and g + Angle between g and h + Angle between h and i + Angle between i and j = 32 + 36 + 45 + 32 + 35 = 180. Hence, e and j are parallel. Correct

Other answers won't satisfy the above property and therefore not parellel

2 Helpful 0 Interesting 0 Brilliant 0 Confused

i am not satisfied to the answer e and j...why?, angle 180 can't affect the legality of principle of parallel between chord e and j...i choose chord a and f...why? because, angle a = 40 and angle f = 36...eliminate chord a and f.....add chord g +h + i + j (45+32+35+30 = 142), compare chord ( e+d+c+b) (32+40+35+35=142), they equal in rotation...so chord a and chord f are PARALLEL..I WANT A REPLY TO THE ONE WHO MAKE THIS PROBLEM...THANK YOU...

Kenneth Ray Morôn - 6 years, 7 months ago
Ravi Kumar
Nov 4, 2014

add the exterior angles and if sum is 180 then the two chords are parallel

0 Helpful 0 Interesting 0 Brilliant 0 Confused

make the starting line your reference and start traversing till you reach the ending line i.e you need to add up those 'deflection angles' in between the lines, if the sum is 180 -the lines are parallel . Do it for all the options until you get the right answer.

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