My Math Forum How deep will a circle sit into a right angle

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 April 14th, 2015, 04:36 AM #1 Newbie   Joined: Apr 2015 From: UK Posts: 3 Thanks: 0 How deep will a circle sit into a right angle Hi, I'm building a toy for my kids whereby a table tennis ball is going to run along troughs made from right-angled pvc corner pieces. The troughs will be held in place by magnetic struts. I need to cut through the corner pieces to have slots into which the struts can be places on which the pvc will sit. The table tennis balls are 40mm in diameter the pvc sides are 25mm in length either side. How far in can/should my slots be in order to give maximum support, without risking the balls getting stuck on the struts? I know the hypotenuse is sqrt(2*25mm^2) ~ 35mm. I know the equation for the arc of a circle sqrt(r^2 - x^2), but I can't figure how to combine the two to get the deepest point that the circle/sphere will reach, or indeed, if this is the correct approach. Any ideas? Last edited by skipjack; April 14th, 2015 at 08:36 AM.
 April 14th, 2015, 06:05 AM #2 Newbie   Joined: Apr 2015 From: UK Posts: 3 Thanks: 0 OK, think I figured it. Of course it's noting to do with the size of the pvc (as it's greater than the radius of the sphere), so it's just the hypotenuse of a 20mm X 20m right-angled triangle minus the radius of the 20mm circle ~ sqrt((400 + 400)) - 20 ~ 8.28mm Last edited by skipjack; April 14th, 2015 at 08:34 AM.
 April 14th, 2015, 08:37 AM #3 Global Moderator   Joined: Dec 2006 Posts: 20,755 Thanks: 2137 That seems correct. What will the magnetic struts be magnetically adhering to?
 April 19th, 2015, 12:55 PM #4 Newbie   Joined: Apr 2015 From: UK Posts: 3 Thanks: 0 I'm going to attach the magnets to a large magnetic white-board, at first at least. I'm hoping to make something like this, if the first iteration is successful: https://www.facebook.com/rob.bane/vi...2863841555656/ i.e. with a larger surface, but struggling to find a cost-and-weight effective large magnetic surface: Last edited by robbane28; April 19th, 2015 at 01:00 PM. Reason: typo

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