Symbiosis National Aptitude Test SNAP 2018 Paper

Let A, B and C be the vertices of three cones of radiur r each
And ‘O’ be the centre of the circle passing through
the points A, B and C
Radius of the circle OA = OB = OC
From AABC, AB = BC = CA = 2 r
AABC is a equilateral triangle

AD is ⊥ from A to BC
then, CD = r
AD = $\sqrt{{\left(\mathit{A}\mathit{C}\right)}^2-{\left(\mathit{C}\mathit{D}\right)}^2}$
= $\sqrt{{\left(2\mathit{r}\right)}^2-{\mathit{r}}^2}$
= $\sqrt{3}\mathit{r}$
Now, AO = $\frac{2}{3}$ × AD (Since AD is median)
AO = $\frac{2}{3}\times \sqrt{3}\mathit{r}$
= $\frac{3}{\sqrt{3}}\left(\mathit{r}\right)$
= 1.15 (r)
Hence, radius of the circle will be larger then r