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Question Number 183185 by mnjuly1970 last updated on 22/Dec/22

	Answered by mr W last updated on 23/Dec/22

	Commented by mr W last updated on 23/Dec/22

	$O A = r_{1} + r_{2} - r_{1} = r_{2}$ $O B = r_{1} + r_{2} - r_{2} = r_{1}$ $O C = r_{1} - r_{2}$ ${(r_{1} + R)}^{2} - {(r_{1} - R)}^{2} = {(r_{1} + r_{2} - R)}^{2} - {(r_{1} - r_{2} - R)}^{2}$ ${R r}_{1} = (r_{1} - R) r_{2}$ $\Rightarrow R = \frac{r_{1} r_{2}}{r_{1} + r_{2}} ✓$
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