geometry

[sunilrawat]

In above figure, AC and AD divide angle EAB into three non-overlapping angles that are equal in measure. Is AB = AE?
1. AD=AC
2. AC=BC

[sunilrawat]

OA A

[top_business_2011]

In above figure, AC and AD divide angle EAB into three non-overlapping angles that are equal in measure. Is AB = AE?
1. AD=AC
2. AC=BC

Angle EAD = Angle DAC = Angle CAB, and let's represent them by 'x'

Required: Is length EA = AB

Statement 1: AD=AC
This means, angle ADC and angle ACD are equal, and let's call them 'y'.
Use the formula: the sum of the two internal angles = the outer angle.
: angle CDA + DAC = angle BCA. Similarly, angle DCA + angle CAD = angle ADE
= y + X = angle BCA. Similarly, y + x = angle ADE
So angle BCA = angle ADE
Now look at triangle AED and triangle ABC. See that? They have two equal corresponding angles; hence, their other corresponding angles must be equal. That is, angle AED = angle ABC. It follows from this that length of AE = Length of AB. Sufficient.

Statement 2: AC = CB
So angle CBA = angle CAB = X
This tells us that angle DCA= 2X [Using the same formula used above]
Similarly, angle EDA = 2X + X = 3X.

So triangle EDA has angle measures of X, 3X, and the unknown angle DEA.
All we can tell here is the sum of X, 3X, angle DEA = 180.
What is angle DEA? It can be x, in which case x =36, and in this case AE= AB, OR it can be 2x, in which case X = 30. And in this case, AE is not equal to AB.
Hence, Insufficient.

Sorry, if I haven't been that clear. You know....

[sunilrawat]

Ahh, I missed x=36.
I was getting a "no" from statement 2.

In above figure, AC and AD divide angle EAB into three non-overlapping angles that are equal in measure. Is AB = AE?
1. AD=AC
2. AC=BC

Angle EAD = Angle DAC = Angle CAB, and let's represent them by 'x'

Required: Is length EA = AB

Statement 1: AD=AC
This means, angle ADC and angle ACD are equal, and let's call them 'y'.
Use the formula: the sum of the two internal angles = the outer angle.
: angle CDA + DAC = angle BCA. Similarly, angle DCA + angle CAD = angle ADE
= y + X = angle BCA. Similarly, y + x = angle ADE
So angle BCA = angle ADE
Now look at triangle AED and triangle ABC. See that? They have two equal corresponding angles; hence, their other corresponding angles must be equal. That is, angle AED = angle ABC. It follows from this that length of AE = Length of AB. Sufficient.

Statement 2: AC = CB
So angle CBA = angle CAB = X
This tells us that angle DCA= 2X [Using the same formula used above]
Similarly, angle EDA = 2X + X = 3X.

So triangle EDA has angle measures of X, 3X, and the unknown angle DEA.
All we can tell here is the sum of X, 3X, angle DEA = 180.
What is angle DEA? It can be x, in which case x =36, and in this case AE= AB, OR it can be 2x, in which case X = 30. And in this case, AE is not equal to AB.
Hence, Insufficient.

Sorry, if I haven't been that clear. You know....

[prateek_guy2004]

Its a Kaplan question ,just did that last week

Answer A

[navami]

IMO A