Mathematics, 16.01.2021 16:50 KenzieD7876
Find the length of the tangent segment AB to the circles centered at O and O' whose radii are a and b respectively when the circles touch each other
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![\Rightarrow (a+b)^2=(a-b)^2+(O' D)^2\\\Rightarrow a^2+b^2+2ab-a^2-b^2+2ab=(O' D)^2\\\Rightarrow 4ab=(O' D)^2\\\Rightarrow O'D=2\sqrt{ab} \\\Rightarrow O' D=2\sqrt{ab}=AB \quad \quad [\because O' DAB\;\; \text{is a rectangle.}]](/tpl/images/1041/6816/ac14a.png)
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Find the length of the tangent segment AB to the circles centered at O and O' whose radii are a and...
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