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Two circles of radii a and b (a < b) touch externally. Length of the direct common tangent from the point of intersection of the direct common tangents to the smaller circle is |
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Answer» `/_ ABM~~/_PQM` (AAA) `(BM)/(QM)=(AB)/(PQ)=b/a` `(BQ+QM)/QM=b/a` -(1) AX=AB-XB =b-a In `/_AXP` BQ=PX=`sqrt(AP^2-AX^2)` =`sqrt((a+b)^2-(b-a)^2)` =`sqrt(4ab)` =`2sqrt(ab)` from eqation 1 `(2 sqrt(ab)+QM)/(QM)=b/a` `(2 sqrt(ab))/(QM) +1=b/a` `(2 sqrt(ab))/(QM)=(b-a)/a` QM=`(2a sqrt(ab))/(b-a)` |
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