A need this question to be solved urgently

three circles of radius 1 cm each are circumcentered by a circle of unknown radius.find the radius of bigger circle

#Geometry

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Comments

The general formula is $\huge R = \frac{r[1 + \sin(\frac{\pi}{n})]} {\sin(\frac{\pi}{n})}$ where $r,R$ and $n$ are the radius of the inner circle, radius of the outer circle and number of circles inscribed within the larger circle respecticely.

Substituting we get the radius of the outer circle $\approx 2.1547$ cm. Try proving the formula of your own!

A Former Brilliant Member - 5 years, 8 months ago

An other way using basic knowledge is like this: Join centres of small circle to obtain an equilateral triangle. Then simply find length of centroid using basic trigonometry or Pythagoras theorem. When that length is found add the radius of small circle to it. As the centroid of triangle is the center of bigger circle.

Sachin Vishwakarma - 5 years, 8 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$