The common chord of two intersecting circles c1 and c2 can be seen from their centres at the angles of 90º and 60º respectively. If the distance between their centres is equal to \sqrt{3} + 1 then the radii of c1 and c2 are :

Engineering

Mathematics

A Circle

Chord of Contact Of Circle

Question

The common chord of two intersecting circles c₁ and c₂ can be seen from their centres at the angles of 90º and 60º respectively. If the distance between their centres is equal to $\sqrt{3}$ + 1 then the radii of c₁ and c₂ are :

$\sqrt{2}$ and 2 $\sqrt{2}$

$\sqrt{2}$ and 2

2 $\sqrt{2}$ and 4

$\sqrt{3}$ and 3

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$\frac{y}{\sin 60 °}$ = $\frac{x}{\sin 30 °}$ ⟹ y = $\sqrt{3}$ x ; y + x = $\sqrt{3}$ + 1

and x $(\sqrt{3} + 1)$ = $\sqrt{3}$ + 1 ⟹ x = 1
⟹ r₁ = x $\sqrt{2}$ = $\sqrt{2}$ and r₂ = 2

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