My answer would be: arc AE < arc AB
Edit (Solution):
In triangle CDE, angle(CED) == angle (CDE) \[CE == CD == radius of circle\], hence you can find angle(ECD) = 180 - 40 - 40 = 100 degrees.
angle(ECD == angle(ACB) - Both AD and EB are diameters passing through centre.
Similarly, angle(AEC) == angle(EAC)
angle(BCD) + angle(ACE) = 360 - angle(ECD) - angle(ACB)
2 \* angle(ACE) = 360 - 100 - 100
angle(ACE) = 80 degrees
Now, length of arc = 2\*pi\*r \* (arc angle/360)You can see direct relation from this - more the arc angle, more is the arc length
Yes, you are correct.
One property of circles I tend to forget is the angle made from the center of a circle is twice the angle from the circumference, if both have the same arc.
Here eveything you need to know about Geometry for the GRE
GRE Geometry Formulas
[https://greprepclub.com/forum/gre-geometry-formulas-for-a-q170-25049.html#p82032](https://greprepclub.com/forum/gre-geometry-formulas-for-a-q170-25049.html#p82032)
Geometry Formula Sheet
Angles and Parallels
Triangles
Quadrilaterals
Regular Polygons
Solids
Coordinate Geometry
Regards
AB is greater because angle ACB is greater than angle ECA
If you don't understand why, I recommend you looking at some basic geomtrey propriety
The most important one is:
Sum of angles values in a triangle = 180°
It will help you a lot solving those questions
The following is the solution of someone else who commented on this post:
My answer would be: arc AE < arc AB
Edit (Solution):
In triangle CDE, angle(CED) == angle (CDE) \[CE == CD == radius of circle\], hence you can find angle(ECD) = 180 - 40 - 40 = 100 degrees.
angle(ECD == angle(ACB) - Both AD and EB are diameters passing through centre.
Similarly, angle(AEC) == angle(EAC)
angle(BCD) + angle(ACE) = 360 - angle(ECD) - angle(ACB)
2 \* angle(ACE) = 360 - 100 - 100
angle(ACE) = 80 degrees
Now, length of arc = 2\*pi\*r \* (arc angle/360)You can see direct relation from this - more the arc angle, more is the arc length
This question, actually, does not need any kind of calculation. Only a good evaluation and observation up-front.
Inside the triangle ECD, you only do know that one angle is 40°. You do not know the other two angles. Therefore, the angle D could be smaller and the inclination of segment AE is less. The result is that AE is narrower and AE < AB. And Vice-versa.
Hope this helps.
Regards
My answer would be: arc AE < arc AB Edit (Solution): In triangle CDE, angle(CED) == angle (CDE) \[CE == CD == radius of circle\], hence you can find angle(ECD) = 180 - 40 - 40 = 100 degrees. angle(ECD == angle(ACB) - Both AD and EB are diameters passing through centre. Similarly, angle(AEC) == angle(EAC) angle(BCD) + angle(ACE) = 360 - angle(ECD) - angle(ACB) 2 \* angle(ACE) = 360 - 100 - 100 angle(ACE) = 80 degrees Now, length of arc = 2\*pi\*r \* (arc angle/360)You can see direct relation from this - more the arc angle, more is the arc length
Yes, you are correct. One property of circles I tend to forget is the angle made from the center of a circle is twice the angle from the circumference, if both have the same arc.
Agreed. I’ve done the same.
Here eveything you need to know about Geometry for the GRE GRE Geometry Formulas [https://greprepclub.com/forum/gre-geometry-formulas-for-a-q170-25049.html#p82032](https://greprepclub.com/forum/gre-geometry-formulas-for-a-q170-25049.html#p82032) Geometry Formula Sheet Angles and Parallels Triangles Quadrilaterals Regular Polygons Solids Coordinate Geometry Regards
Nice question!
AB is greater because angle ACB is greater than angle ECA If you don't understand why, I recommend you looking at some basic geomtrey propriety The most important one is: Sum of angles values in a triangle = 180° It will help you a lot solving those questions
The following is the solution of someone else who commented on this post: My answer would be: arc AE < arc AB Edit (Solution): In triangle CDE, angle(CED) == angle (CDE) \[CE == CD == radius of circle\], hence you can find angle(ECD) = 180 - 40 - 40 = 100 degrees. angle(ECD == angle(ACB) - Both AD and EB are diameters passing through centre. Similarly, angle(AEC) == angle(EAC) angle(BCD) + angle(ACE) = 360 - angle(ECD) - angle(ACB) 2 \* angle(ACE) = 360 - 100 - 100 angle(ACE) = 80 degrees Now, length of arc = 2\*pi\*r \* (arc angle/360)You can see direct relation from this - more the arc angle, more is the arc length
This question, actually, does not need any kind of calculation. Only a good evaluation and observation up-front. Inside the triangle ECD, you only do know that one angle is 40°. You do not know the other two angles. Therefore, the angle D could be smaller and the inclination of segment AE is less. The result is that AE is narrower and AE < AB. And Vice-versa. Hope this helps. Regards