Tangents are drawn from any point on the circle $x^{2} + y^{2} = R^{2}$ to the circle $x^{2} + y^{2}

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Tangents are drawn from any point on the circle $x^{2} + y^{2} = R^{2}$ to the circle $x^{2} + y^{2} = r^{2}$. If the line joining the points of intersection of these tangents with the first circle also touch the second, then $R$ equals:

Accepted Answer

[Key Concept: Tangents from a point on $x^{2} + y^{2} = R^{2}$ to $x^{2} + y^{2} = r^{2}$: the chord of contact has a fixed length.]$r = Rcos60^{\circ} = \frac{R}{2}$

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