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In the figure above, the vertices of triangle ABC lie on the circumfer

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In the figure above, the vertices of triangle ABC lie on the circumfer  [#permalink]

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New post 26 Dec 2013, 05:01
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A
B
C
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Difficulty:

  25% (medium)

Question Stats:

74% (01:04) correct 26% (01:16) wrong based on 138 sessions

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In the figure above, the vertices of triangle ABC lie on the circumference of circle O. What is the value of x?

(A) 35
(B) 45
(C) 55
(D) 65
(E) 70


I'm puzzled. If one solve for angle AOB, it would imply a different result. Why?
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Re: In the figure above, the vertices of triangle ABC lie on the circumfer  [#permalink]

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New post 26 Dec 2013, 05:20
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1
nechets wrote:
Image

In the fi…gure above, the vertices of triangle ABC lie on the circumference of circle O. What is the value of x?

(A) 35
(B) 45
(C) 55
(D) 65
(E) 70


I'm puzzled. If one solve for angle AOB, it would imply a different result. Why?


All angels:
Image
Notice that OB = OC = radius, thus triangle OBC is isosceles. Therefore angle OCB = angle OBC --> x + x + 70° = 180° --> x = 55°.

Answer: C.

Hope it's clear.

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Imagem1.jpg
Imagem1.jpg [ 27.04 KiB | Viewed 2205 times ]

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Re: In the figure above, the vertices of triangle ABC lie on the circumfer  [#permalink]

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New post 30 Jan 2018, 23:50
nechets wrote:

In the figure above, the vertices of triangle ABC lie on the circumference of circle O. What is the value of x?

(A) 35
(B) 45
(C) 55
(D) 65
(E) 70


I'm puzzled. If one solve for angle AOB, it would imply a different result. Why?


Solution



Image

    • Assuming the O is the center of the circle and AC is the diameter.
      o We can infer that the lines OB = OC = OA = radius of the circle.
    • Let us focus on the triangle OBC, in which OB = OC.
      o Since, it is an isosceles triangle
      o Angle OBC = Angle OCB = x
      o And we know that angle BOC = 70
    • Per our conceptual understanding –
      o Sum of internal angles of a triangle = 180
      o Thus, for triangle OBC, we can write
         70 + x + x = 180
         2x = 110
         x = 55
    • Thus, the correct answer is Option C.

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Re: In the figure above, the vertices of triangle ABC lie on the circumfer  [#permalink]

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New post 31 Jan 2018, 15:56
nechets wrote:
Image

In the figure above, the vertices of triangle ABC lie on the circumference of circle O. What is the value of x?

(A) 35
(B) 45
(C) 55
(D) 65
(E) 70



Since sides OC and OB are radii, side OC = side OB, creating an isosceles triangle, and thus angle OCB = angle OBC = x.

Thus, we have:

2x + 70 = 180

2x = 110

x = 55

Answer: C
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Re: In the figure above, the vertices of triangle ABC lie on the circumfer  [#permalink]

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New post 24 Oct 2018, 01:22
1
nechets wrote:
Image

In the figure above, the vertices of triangle ABC lie on the circumference of circle O. What is the value of x?

(A) 35
(B) 45
(C) 55
(D) 65
(E) 70


I'm puzzled. If one solve for angle AOB, it would imply a different result. Why?


Dear Moderator,
The figure of the above question is not visible , hope you will look into this. Thank you.
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Re: In the figure above, the vertices of triangle ABC lie on the circumfer  [#permalink]

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New post 24 Oct 2018, 02:00
stne wrote:
nechets wrote:
Image

In the figure above, the vertices of triangle ABC lie on the circumference of circle O. What is the value of x?

(A) 35
(B) 45
(C) 55
(D) 65
(E) 70


I'm puzzled. If one solve for angle AOB, it would imply a different result. Why?


Dear Moderator,
The figure of the above question is not visible , hope you will look into this. Thank you.


__________________
Fixed that. Thank you.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: In the figure above, the vertices of triangle ABC lie on the circumfer &nbs [#permalink] 24 Oct 2018, 02:00
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