May 6th, 2017, 06:43 AM  #1 
Newbie Joined: May 2017 From: India Posts: 1 Thanks: 0  Q19
How to solve question 19

May 6th, 2017, 12:54 PM  #2 
Global Moderator Joined: Dec 2006 Posts: 18,584 Thanks: 1488 
Have you drawn a diagram that's roughly to scale?

May 6th, 2017, 03:10 PM  #3 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 11,662 Thanks: 740 
Try this: draw circle diameter 30 with center A(15,15) draw circle diameter 20 with center B(10,15) draw circle diameter 10 with center C(25,15) Now draw cutout circle diameter 2r with center D(x,y) such that it is tangent to all 3 circles above Draw triangle BCD; sides will be: CD = 5+r, BD = 10+r, BC = 15 Have fun... 
May 6th, 2017, 05:14 PM  #4 
Global Moderator Joined: Dec 2006 Posts: 18,584 Thanks: 1488 
It turns out that 2r = 8 4/7 m.

May 6th, 2017, 06:35 PM  #5 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 11,662 Thanks: 740 
So if the 3 circles had diameters of 210, 140 and 70, then cutout circle = diameter 60 
May 8th, 2017, 12:28 PM  #6 
Member Joined: Dec 2016 From: United States Posts: 53 Thanks: 3 Math Focus: Abstract Simulations  
May 8th, 2017, 12:36 PM  #7 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 11,662 Thanks: 740  
May 8th, 2017, 01:26 PM  #8 
Member Joined: Dec 2016 From: United States Posts: 53 Thanks: 3 Math Focus: Abstract Simulations 
Oh. I thought you were telling him to guesstimate.

May 8th, 2017, 01:44 PM  #9 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 11,662 Thanks: 740 
I'm sure skipjack was giving him an appropriate hint...
Last edited by skipjack; May 9th, 2017 at 01:45 AM. 
May 9th, 2017, 01:44 AM  #10 
Global Moderator Joined: Dec 2006 Posts: 18,584 Thanks: 1488 
A good estimate suffices for this multiple choice question. The exact value can easily be found by use of this theorem. 