Find Radius of Largest Circle in Middle - IGCSE Math

[salik]

The large circle has a radius of 10cm. Find the radius of the largest circle which will fit in the middle.


I am doing my IGCSE right now and this question has proved a bit difficult for me and my friends .I asked a few math teachers in our school and they couldn't solve it as well. I guess someone here could help.

Thanks

http://img2.freeimagehosting.net/uploads/ee0a88b423.jpg

 

[NateTG]

Draw in the square formed by the centers of the smaller circles, and a diameter of the large circle that goes through two corners of the square.

 

[light_bulb]

radius - diameter of one the smaller circles = the radius of the largest circle that can fit in the middle of all the circles.

 

[light_bulb]

i noticed the bomb, explain how that is wrong?

 

[salik]

umm,how do i find the diameter of the smaller circles?.. I am a bit confused here

 

[light_bulb]

a ruler will work.

 

[salik]

This is a diagram in my textbook and it is not to scale. It is part of the chapter in which we learn how to find areas of circles,so I am pretty sure the answer is supposed to be found using a formula and not a ruler.

The answer given in the answers section is 1.716 cm. Hope this helps

 

[light_bulb]

pi * radius^2 = area
area / 4 = x
sqrt(x) = y
y = diameter of small circle

at least that's how i hope it's done.

 

[hage567]

Look at NateTG's post, that's the best way. In the square, form a right angled triange. Use Pythagoras to get the relation between all the sides. Then use his other tip about writing out the diameter of the large circle in terms of the smaller circles. That gives you enough info to solve. You don't need to worry about areas at all.

 

[mikp2527]

you can find the radius of the smaller circle using this method(please view diagram)
Large circle radius 10cm
Medium circle radius x
Small circle radius Y
(sq)AB=(sq)2X+(sq)2X=(sq)4x+(sq)4X
(sq)AB=(sq)8X
AB=2(sqrt)2X
2X+2Y=2(sqrt)2X
AB=2x+2Y
20=2X=2Y+2X=4X+2Y
2Y=20-4X
Y=10-2X
2X=10-Y
X=(10-Y)/2
2X+2Y=2(sqrt)2X
2(10-Y/2)+2Y=2(sqrt)2(10-Y/2)
10-Y+2Y=(sqrt)2(10-Y)
10+Y=10(sqrt)2-10
Y(1+(sqrt)2)=10((sqrt)2-1)
Y=10((sqrt)2-1)/(1+(sqrt)2)
Y=10(1.4142-1)/(1+1.4142)
Y=10(0.4142)/(2.4142)
Y=4.142/2.4142
Y=1.7156
Y=1.716

hope this helps

 

[Kaushikmehul]

X is radius of medium circle
a^2+b^2=c^2
2x^2+2x^2=[20-2x]^2
8x^2=[20-2x]^2
After solving u get
X=4.142135624
X. 2
_______________
8.284271247

10-8.284=
1.716cm