# Two Circle Problems

• March 22nd 2013, 12:19 PM
Two Circle Problems
How do you do these two problems? (note: they are lifted from: a site called regentsprep.org).

I feel like #6 is on the tip of my pencil. But I can't quite piece the info together. Circle 1 is x^2+y^2=16 and circle 2 is x^2+y^2=100. There must be some relationship (never mind that I reused x).

But #7 seems like there isn't enough information, no matter how many new radii or inscribed angles I draw, I can't find any useful information.
• March 22nd 2013, 12:31 PM
earboth
Re: Two Circle Problems
Quote:

How do you do these two problems? (note: they are lifted from: a site called regentsprep.org).

I feel like #6 is on the tip of my pencil. But I can't quite piece the info together. Circle 1 is x^2+y^2=16 and circle 2 is x^2+y^2=100. There must be some relationship (never mind that I reused x).

But #7 seems like there isn't enough information, no matter how many new radii or inscribed angles I draw, I can't find any useful information.

to #6: Draw the cross-section of the sphere. Use Pythagorian theorem.

to #7: Do you know what this sign means: $\cong$
• March 22nd 2013, 12:33 PM
ebaines
Re: Two Circle Problems
#6 is easier than you think! You have a right angle triangle with one node from the center of the sphere , another at the center of the slice, and a third at the intersection of the slice and the edge of the spehere. You know the values for the radius of the sphere and the circle, so use Pythagoras to find x.

Attachment 27649

#7 is so obvious you're just not seeing it. It would be similar to a problem like this: if x=y, and x=8, what is y?
• March 22nd 2013, 12:47 PM
Re: Two Circle Problems
Quote:

Originally Posted by earboth
to #6: Draw the cross-section of the sphere. Use Pythagorian theorem.

to #7: Do you know what this sign means: $\cong$

Congruent (it's like equals for objects). It means all the properties of one object match all the properties of the other object (except for position).
• March 22nd 2013, 12:53 PM