QR-162

[[email protected]]

Please help me understand the geometry rules involved in the calculation.


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

Thanks

[kevincanspain]

How many isosceles triangles do you see?

[Atekihcan]

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

[[email protected]]

I know Atekihcan but have more doubts! And need to look at the problem n a different way!

[[email protected]]

Hi Kevin,

In total there are 3 Isosceles triangles!

[GMATGuruNY]

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:


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.

[[email protected]]

Thanks Mitch for making it so simple!


Regards
Shiba

[Brent@GMATPrepNow]

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°


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