Quant Review #153

[lsegal]

The point R,T, and U lie on a circle that has a radius 4. If the length of arc RTU is 4pie/3, what is the length of line segment RU.

a) 4/3
b)8/3
c)3
d)4
e)6



I understand how to get the answer, but my confusion comes from the idea that in order for a triangle to be inscribed in a circle, the triangle needs to have a right angle. Obviously not in this case, but I'm baffled as to why (not that it takes all that much to baffle me....)

[RonPurewal]

my confusion comes from the idea that in order for a triangle to be inscribed in a circle, the triangle needs to have a right angle.

this is true if, and only if, the inscribed angle cuts off a semicircle (i.e., the sides of the angle hit the circle at two points that make a semicircle/diameter).

more generally, the measure of an inscribed angle is half of whatever arc it cuts off. (you can probably find a zillion illustrations of this idea, with diagrams and so on, by googling the term "inscribed angle".)

[lsegal]

Thanks. Can't believe I didn't see that. Loving your recordings btw....

[RonPurewal]

Thanks. Can't believe I didn't see that. Loving your recordings btw....

thanks.

[hkparikh09]

I had trouble on this question as well.

Is the inscribed triangle an equilateral triangle because two of its sides have to be the radius (length of 4)? The central angle = 60 degrees, and another angle must also = 60 degrees since two sides are the same (radius). If two sides and two angles are the same, then the 3rd side and angle must also be the same.

I know I didn't explain that very well, but can you tell me if my understanding is correct?

[RonPurewal]

I now realize that "Quant Review" refers to the OG quant supplement. (I must not have realized this when I answered the original post.)

We can't allow OG problems on the forum, so this thread is now locked.