In the adjoining figure, AB is the chord of the larger circle touching the smaller circle. The centre of both the circles is O. If $AB = 2r$ and $OP = r$, then the radius of larger circle is:

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Question

In the adjoining figure, AB is the chord of the larger circle touching the smaller circle. The centre of both the circles is O. If $AB = 2r$ and $OP = r$, then the radius of larger circle is:

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Accepted Answer

Step 1: AB is tangent to inner circle at P, so $OP \perp AB$. $AP = r$. In right $	riangle OPA$: $OA^2 = OP^2 + AP^2 = r^2 + r^2 = 2r^2$. $OA = r\sqrt{2}$.

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