If A is the centre of the circle, what is the value of x ?

Question

Are You Up For the Challenge: 700 Level Questions https://gmatclub.com/forum/download/file.php?id=53120 If A is the centre of the circle, what is the value of x ? (1) AD = BD = CD (2) y = 60 Are You Up For the Challenge: 700 Level Questions circlecircle.JPG

GMATinsight · Answer

Angle ABC = Angle BDC (ABC is an isosceles triangle)

Statement 1 : AD = BD = CD = Radius

i.e. Triangle ACD is an equilateral triangle
Also, Triangle ABD is an equilateral triangle

i.e. x = (1/2)Triangle ABD = 30

SUFFICIENT

Statement 2 : y = 60

But BD is unknown hence triangle ABD can be equilateral or otherwise hence

NOT SUFFICIENT

Answer: Option A

freedom128 · Answer

Radius: AB = AC = AD

(1) AD = BD = CD
This shows that triangles ABD and ADC are both equilateral triangles and y=60 deg. We can easily deduce that x=30 deg.
SUFFICIENT.

(2) y = 60
This shows that triangle ADC is an equilateral triangle, but ABD may or may not be an equilateral triangle. We cannot deduce x value.
NOT SUFFICIENT

FINAL ANSWER IS (A)

GMATWhizTeam · Answer

Solution 
 Step 1: Analyse Question Stem 
 • AB = AC = AD  
• In triangle ABC, AB = AC
 o ABC is an isosceles triangle
o ∠ABC = ∠ACB = x  
We need to find the value of x
 Step 2: Analyse Statements Independently (And eliminate options) – AD/BCE 
 Statement 1:  AD = BD = CD
 • In triangle ABD, we have
 o AB= AD = CD
o ABD is an equilateral triangle.
o ∠ABD =∠ADB=∠BAD =60 
• Similarly, ACD is an equilateral triangle.
 o ∠ACD =∠ADC =∠CAD =60 
• ∠BAD =60
• ∠BCD = 30
 o ∠ACB = x =60-30=30
o x =30  
Hence, statement 1 is sufficient, we can eliminate answer options B, C, and E.
 Statement 2:  y = 60
 • We can infer that ACD is an equilateral triangle.
 o But we can’t find the value of x with this information.  
Hence, statement 2 is not sufficient, the correct answer is  Option B

exc4libur · Answer

(1) sufic 
triangles are equilateral, x=1/2*60=30

(2) insufic

Ans (A)

unraveled · Answer

If A is the centre of the circle, what is the value of x ? (1) AD = BD = CD (2) y = 60 Circle ABCD.png Please spare my bad writing and diagrams. Answer A.

Jawad001 · Answer

Solution:
From statement (1), AD = BD = CD, 
Here, AD = radius = BD = CD, so ABD is an equilateral triangle.
ABD = 60, Therefore, x= 30. Sufficient.

From statement (2), AC = AD = DC
Therefore, value of x can be determined. Sufficient. 
Answer: D

jrk23 · Answer

is c is the answer. As b alone can't be possible with A we can deduce similarity but can't find angle So we need both to answer the question.

lacktutor · Answer

If A is the centre of the circle, what is the value of x ?

(Statement1) : AD = BD = CD
—> triangle ABD and triangle ACD are equilateral triangles. 
When joining both of them, a rhombus is created.
—> Diagonals of the rhombus are a perpendicular to each other. 
Well, it’s clear that x is equal to 30 degrees. 
 Sufficient

(Statement2) : y = 60
—> triangle ACD is an equilateral triangle. But we are not sure whether triangle ABD is the same as triangle ACD. 
No info about what kind of triangle ABD is 
 Insufficient

The answer is A.

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Kody · Answer

1. must be sufficient because it is telling us that triangle ABD is an equilateral triangle that is being bisected by line BC, thus x is equal to 30 degrees 
2. must also be sufficient because we know that AD is equal to AC, eluding to the fact that triangle ADC is an equilateral triangle. ABD must be similar to ADC.

someone correct me if I am wrong here.

bumpbot · Answer

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If A is the centre of the circle, what is the value of x ?

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