Grade 11Analytical Geometry
Two circles with radii r1 and r2 touch externally. What is the length of their direct common tangent?
Two circles with radii r1 and r2 touch externally. What is the length of their direct common tangent?
3 Answers
Jitender K Yadav
Just draw two circles with centers C and C`, which touch each other at P. (Draw Figure yourself as per instructions.)The direct common tangent PP` has length `d`.CC`=r1+r2Draw PP1||CC` with P1 on C`P`.CP||C`P` (tangent common)Thus CPP1C` is a ||gm.Thus, PP1=CC`=r1+r2P`P1=C`P`-P1P`=r2-r1Since, PP` is perpendicular to P`P1,d=√[(r1+r2)^2-(r2-r1)^2]=√[4r1r2]=2√(r1r2)
gurram meghana
The formula for the above question is 2(r1)(r2)/ r1+r2. Therefore the solution for the above Question is 2(1)(2)/1+2=4/3
gurram meghana
The formula to the above question is 2(r1)(r2)/r1+r2. Therefore the solution to the above question is 2(1)(2)/1+2=4/3.
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