BTW the general case of n circles arranged in a row under a semicircle is interesting. If you want to try that yourself stop reading. I found the answer to be this: if the semicircle's radius is R and the small circles' radii are all r, and there are n circles, R/r = sqrt(n^2-2n+2)+1.
Oh hey not to be a pest, but this reminded me of another circle puzzle I don't think you've done. Dunno if you are making new geometry videos but if so this is a goodie and right up your alley. Two circles with radius 2 are tangent. Let's say one is on the left and one is on the right, Above them and tangent to both is a circle with radius 1. These three circles are all themselves tangent to a larger circle that encompasses them. There is a fourth circle at the bottom that is tangent to the circumcircle and the two r=2 circles. What's its radius?
Hey Qermaq, you'll never be a pest! 😉 I love your comments even though I'm unable to respond to all. I know you've been around for a long time and I hope to see you when we reach millions! Thank you for your support and amazing ideas! Please keep 'em coming. Looks good to me! I'll take a look at this idea. 💖🥰
@@ShortsOfSyber you bet. BTW it might be easier to start with the radius 1 circle being a radius 2 circle. Makes finding the circumradius a bit easier.
BTW the general case of n circles arranged in a row under a semicircle is interesting. If you want to try that yourself stop reading. I found the answer to be this: if the semicircle's radius is R and the small circles' radii are all r, and there are n circles, R/r = sqrt(n^2-2n+2)+1.
thanks sir
Most welcome
Rule of thumb: whenever you see two circles that are tangent, always draw a line passing through the centers. It always leads to something.
👍💪🤩
There's also (√5-1)x/4 in the first solution, not (√5-2)x/4 :)
Possible that the 2 in the numerator was missed when reducing the fraction /8
I think there's a mistake at 4:40 when dividing by 8
Oh hey not to be a pest, but this reminded me of another circle puzzle I don't think you've done. Dunno if you are making new geometry videos but if so this is a goodie and right up your alley.
Two circles with radius 2 are tangent. Let's say one is on the left and one is on the right, Above them and tangent to both is a circle with radius 1. These three circles are all themselves tangent to a larger circle that encompasses them. There is a fourth circle at the bottom that is tangent to the circumcircle and the two r=2 circles. What's its radius?
Hey Qermaq, you'll never be a pest! 😉
I love your comments even though I'm unable to respond to all.
I know you've been around for a long time and I hope to see you when we reach millions! Thank you for your support and amazing ideas! Please keep 'em coming. Looks good to me! I'll take a look at this idea. 💖🥰
@@ShortsOfSyber you bet. BTW it might be easier to start with the radius 1 circle being a radius 2 circle. Makes finding the circumradius a bit easier.