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

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Bunuel
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If A is the centre of the circle, what is the value of x ? [#permalink] New post   28 Feb 2020, 02:03
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A
B
C
D
E

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95% (hard)

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32% (02:01) correct 68% (01:59) wrong based on 95 sessions
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If A is the centre of the circle, what is the value of x ?

(1) AD = BD = CD

(2) y = 60


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A
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Re: If A is the centre of the circle, what is the value of x ? [#permalink] New post   28 Feb 2020, 04:08
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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
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Re: If A is the centre of the circle, what is the value of x ? [#permalink] New post   28 Feb 2020, 05:07
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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)
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Re: If A is the centre of the circle, what is the value of x ? [#permalink] New post   28 Feb 2020, 06:26
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Solution


Step 1: Analyse Question Stem


    • AB = AC = AD [radius of the circle]
    • 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
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If A is the centre of the circle, what is the value of x ? [#permalink] New post   Updated on: 02 Mar 2020, 04:08
Quote:
If A is the centre of the circle, what is the value of x ?

(1) AD = BD = CD

(2) y = 60


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

(2) insufic

Ans (A)

Originally posted by exc4libur on 28 Feb 2020, 06:42.
Last edited by exc4libur on 02 Mar 2020, 04:08, edited 1 time in total.
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Re: If A is the centre of the circle, what is the value of x ? [#permalink] New post   28 Feb 2020, 11:09
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If A is the centre of the circle, what is the value of x ?

(1) AD = BD = CD

(2) y = 60
Attachment:
Circle ABCD.png
Circle ABCD.png [ 409.62 KiB | Viewed 2354 times ]


Please spare my bad writing and diagrams.

Answer A.
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Re: If A is the centre of the circle, what is the value of x ? [#permalink] New post   01 Mar 2020, 01:37
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
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Re: If A is the centre of the circle, what is the value of x ? [#permalink] New post   01 Mar 2020, 06:11
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.
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Re: If A is the centre of the circle, what is the value of x ? [#permalink] New post   01 Mar 2020, 11:03
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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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Re: If A is the centre of the circle, what is the value of x ? [#permalink] New post   01 Mar 2020, 11:13
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.
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Re: If A is the centre of the circle, what is the value of x ? [#permalink] New post   28 Apr 2021, 11:21
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