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Source: Beat The GMAT — Problem Solving |
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kevincanspain
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Atekihcan
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You have posted the same problem one week ago and I've already posted a solution there : https://www.beatthegmat.com/qr-161-t231724.html#640620
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GMATGuruNY
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Since OC=AC=AB, we get:
In the figure above, point O is the center of the circle and OC=AC=AB. What is the value of x?
In ∆AOC, y + 2x = 180.
Since y and z form a straight line, y + z = 180.
Thus:
y + 2x = y + z
2x = z.
The result is the following:
Since OA and OB are radii, OA=OB.
Thus, in ∆OAB, the angles opposite OA and OB are equal:
Since the sum of the angles inside ∆OAB = 180, we get:
x + x + x + 2x = 180
5x = 180
x = 36.
The correct answer is B.
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Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
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As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
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Brent@GMATPrepNow
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Since OC = AC, ∆AOC is an isosceles triangle, which means ∠OAC is also x°[email protected] wrote:In the figure above, point O is the center of the circle and OC=AC=AB. What is the value of x?
A) 40
B) 36
C) 34
D) 32
E) 30
Since all 3 angles in ∆AOC must add to 180°, we can conclude that ∠OCA = (180-2x)°
Since angles on a LINE must add to 180°, we can conclude that ∠ACB = 2x°
Since AC = AB, ∆ACB is an isosceles triangle, which means ∠CBA is also 2x°
Finally, since OA and OB are radii of the same circle, we know that ∆OAB is an isosceles triangle, which means ∠OABis also 2x°
At this point, we can see that the 3 angles ∆OAB are x°, 2x° and 2x°
Since the angles in a triangle must add to 180°, we can write: x° + 2x° + 2x° = 180°
Simplify: 5x = 180
Solve: x = 36
Answer: B
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