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Trippzy · Oct 13, 2023

you in year 10 bro relax. enjoy school before u cant

jimmysmith560 · Oct 14, 2023

Would the following working help?

Working said:
$\text{Connect the centres of the 6 circles. Furthermore, connect the centre of each of the 6 circles to the centre of the 7th circle.}$

$\text{Note that there are 6 triangles, and furthermore, they are all isosceles.}$

$\text{Consider the point of the triangle where it touches the 7th circles centre. All these triangles are equal, and therefore:}$

$6 \times\text{(the top angle of the triangle)}\, = 360\,\text{(angles at a point)}$

$\therefore\,\text{The top angle of the triangle} = 60^{\circ}$

$\text{As all these triangles are isosceles, this new information, that is the top angle is 60 degrees, imply that these triangles are infact equilateral triangles}$

$\text{If we let the smaller circles have radius R, then:}$

$2R = r$

$\therefore R = \frac{1}{2}r$

$\text{Let the 7th circle have radius x, then:}$

$\frac{1}{2}r + x = r$

$\therefore x = \frac{1}{2}r$

JiffyVFX · Oct 14, 2023

jimmysmith560 said:
Would the following working help?

yes thanks

JiffyVFX · Oct 14, 2023

Trippzy said:
you in year 10 bro relax. enjoy school before u cant

i doo

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