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by [email protected] » Tue May 14, 2013 3:18 am
Please help me understand the geometry rules involved in the calculation.


Done know how to draw the diagrm here, hence posting the picture!

Thanks
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by kevincanspain » Tue May 14, 2013 4:42 am
How many isosceles triangles do you see?
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by Atekihcan » Tue May 14, 2013 4:50 am
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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by [email protected] » Tue May 14, 2013 5:04 am
I know Atekihcan but have more doubts! And need to look at the problem n a different way!
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by [email protected] » Tue May 14, 2013 10:04 pm
Hi Kevin,

In total there are 3 Isosceles triangles!
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by GMATGuruNY » Wed May 15, 2013 4:23 am
Image

In the figure above, point O is the center of the circle and OC=AC=AB. What is the value of x?
Since OC=AC=AB, we get:
Image

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:
Image

Since OA and OB are radii, OA=OB.
Thus, in ∆OAB, the angles opposite OA and OB are equal:
Image

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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by [email protected] » Wed May 15, 2013 6:35 am
Thanks Mitch for making it so simple!


Regards
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by Brent@GMATPrepNow » Tue Apr 24, 2018 12:29 pm
[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 OC = AC, ∆AOC is an isosceles triangle, which means ∠OAC is also x°
Image

Since all 3 angles in ∆AOC must add to 180°, we can conclude that ∠OCA = (180-2x)°
Image

Since angles on a LINE must add to 180°, we can conclude that ∠ACB = 2x°
Image

Since AC = AB, ∆ACB is an isosceles triangle, which means ∠CBA is also 2x°
Image

Finally, since OA and OB are radii of the same circle, we know that ∆OAB is an isosceles triangle, which means ∠OABis also 2x°
Image

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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