Four Circles In A Circle

• #1

A large circle has a radius of 10 cm. Independent within this circle are four smaller circles of equal size (fitting inside the larger circle exactly). The question asks: Observe the radius of the largest circle which will fit in the middle.

Here is a link to a picture that I've pulled from Google that shows the same diagram as the maths book:

The book answer is: ane.72 cm

My attempt: The distance betwixt the points of touch on of the smaller circles is: 20/3 = half-dozen.66 cm
Then the distance between the indicate of touch of i of the smaller circles and the centre of the larger circle is: half-dozen.66/two = 3.33 cm
Therefore the radius of the smaller circle should also be iii.33 cm
Total diameter of two circles facing diagonally opposite each other is three.33 x four = xiii.32 cm

So the distance remaining between the circles is 20 – thirteen.32 = six.68 cm

So radius if a circle in the middle would be 6.68/2 = 3.34 cm THIS IS THE WRONG Reply

Concluding edited by a moderator: Apr 3, 2015

• #iv

Thank you

Thanks Jonah2.0 your link got me stated towards thesolution: http://world wide web.algebra.com/algebra/homew...on.308572.html

Thanks Dennis. This actually helped:

u = radius of the four circles
5 = radius of added circle

I still need a fiddling more aid with the algebra please. I don't know where I'vegone wrong with my calculation.

As Denis said:

u = radius of the four circles
5 = radius of added pocket-sized circumvolve inthe middle

Radius of big circle = 2u + v = 10

five = x - 2u ....... (i)

A square forms with sides of length u.
It can be separate into a triangle with hypotenuse of length u+v

Then u^two + u² = (u + v)²

METHOD A

2u ^two = (u + v) (u +v)
2u ⁱⁱ = u ² + uv +uv + 5 ^two
u ² =2uv + v ² …… (ii)

Inserting (i) into (ii) :
u ^two = 2u (x-2u) +(10-2u) ²
u ² = 20u - 4u ⁱⁱ +(ten-2u) ^two
5u ⁱⁱ – 20u = (ten-2u) (10-2u)
5u ² – 20u = 100 -20u – 20u + 4u ²
u ⁱⁱ = 100 – 20u ….. Now WHAT Exercise I Practise?I'm stuck

I've besides tried a unlike method:
METHOD B
Earlier I said u^two+ u² = (u + v)ⁱⁱ
And then 2u²= (u + v)²
Square rooting both sides of the equation gives:
u √ ii = u + 5
1.414u = u + five
0.414 = five

v = 10 - 2u ....... (i)
u = (10-v)/two
u = (10-0.414)/2
u =4.793 Wrong Answer

• #5

Figured it out at last. Will post the total solution subsequently sleep because my encephalon is exhausted after all the computing I've been doing the concluding few days.

Answer requires me to utilise the quadratic equation formula

Four Circles In A Circle,

Source: https://www.freemathhelp.com/forum/threads/4-circles-inside-a-smaller-circle-radius-calculation.90953/

Posted by: hurdansten78.blogspot.com

Share this post