Question: Circle with Parallel Lines

Comment on Circle with Parallel Lines

Awesome! How amazing are your explanations. I hope that in the exam day I can do similar approach quicker.

I solved almost similar with slight change:

< AOD = 160 degrees (straight line is 180 degrees)

since AO =OD (equal radii) so < OAD = < ODA = 10 degrees (sum of all sides of triangle is 180 degrees).
Now < OAD = 10 degrees is alternate angle to < ADC which equals to 10 degrees. (alternate angles are equal).

Now we have 2 angles in triangle that has x. So x +90+10 is 180 degrees, sum of all angles of triangle. So x = 80 degrees. Is this correct?
greenlight-admin's picture

Perfect!

Abdul Hannan's picture

Hi Mr Hanneson,

I used a more simple and very very quick approach for solving this question.

STEP I:-
Since minor arc BD is same for both < BOD and < BAD and <BOD is central angle then < BAD = 10 degrees


STEP II:-
Since we know that line AB and line CD are parallel and line AD is a transverse from those parallel lines then <BAD = < ADC That is 10 degrees.

STEP III:-
Since line ED is a diameter then any angle joining ED is right angle and assigning F to denote at the angle x we get a triangle FCD.


NOW to find <CFD=X

NOW <FCD + <CFD + <FDC =180

Now <ADC=<FDC=10 Degrees
<ECD=<FCD=90 Degrees


Solving we get

<DFC =<X =80 Degrees......VOILA

Cheers,
ABDUL HANNAN
greenlight-admin's picture

Voila indeed!!
Great solution, Abdul.

great explanation sir

https://gre.myprepclub.com/forum/the-diameter-of-the-circle-is-3073.html
I already arrived at A before i checked and saw D. This figures not being drawn to scale phenomena is difficult for me to process. Please kindly help with a detailed explanation
greenlight-admin's picture

Here's my full solution: https://gre.myprepclub.com/forum/the-diameter-of-the-circle-is-3073.html...

You're not the only one who is confused. In many cases, the diagrams actually cause more problems (if you believe they're drawn to scale) :-)

Here's a question where the scale is totally off (but it's a GRE-worthy question): https://gre.myprepclub.com/forum/in-the-triangle-abc-what-is-the-value-o...

Cheers,
Brent

Isn't line ED a transversal for the parallel lines which would make the angle at point D 20? Which gives us angle at point E = 180-90-20 = 70. Angle x and angle E hold the same chord so their angles must be equal but 70 is incorrect.
greenlight-admin's picture

All of the steps you took to conclude that ∠CED = 70° are correct.

However, angle x is not an inscribed angle, since the vertex of angle x does not lie ON the circle. Instead, the vertex is INSIDE the circle, which means we can't apply the circle property that says "two INSCRIBED angles containing the same chord must be equal."

Does that help?

Cheers, Brent

Hi Brent,

At the exam, if we would get a problem as this would you recommend us to draw more figures? For example, I found it easier to see the angles formed by the parallel lines when you removed the other lines from the figure. I guess it is a good practice to do this at the exam too, right?
Otherwise, we might not notice them, especially that my figure was drawn really small
greenlight-admin's picture

Hi Carla,

Yes, I definitely recommend redrawing the figure on your noteboard on test day.
Doing so will make it easier to identify and highlight certain aspects of the diagram.

Cheers,
Brent

Have a question about this video?

Post your question in the Comment section below, and a GRE expert will answer it as fast as humanly possible.

Change Playback Speed

You have the option of watching the videos at various speeds (25% faster, 50% faster, etc). To change the playback speed, click the settings icon on the right side of the video status bar.

Let me Know

Have a suggestion to make the course even better? Email us today!

Free “Question of the Day” emails!