InterviewSolution
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InterviewSolution
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Let the point B be the reflection of the point A(2,3) with respect to the line 8x-6y-23=0 Let lceiling_A and lceiling_B respectively. Be circles of radil 2 and I which centres A and B respectively. Let T be a common tangent to the circles lceilingA and lceiling B such that both the circles are on the same side of T. If C is the point of intersection of T and the line passing thorugh A and B, then the length of the line segment AC is ............. |
Answer»  From the figure, `AC=(2)/(sin THETA) .....(i)` `becausesin theta =(1)/(CB)` `(" from "Delta CPB) ......(ii)` ` and sin theta =(2)/(AC)=(2)/(CB+AB)("from "Delta CQA)......(iii)` `because AB=AM+MB=2AM` ` =2(|(8xx2)-(6xx3)-23|)/(sqrt(64+36))=(2xx25)/(10)=500` From Eqs. (ii) and (iii), we get `sin theta=(1)/(CB)=(2)/(CB+AB)` `rArr (1)/(CB)=(2)/(CB+5)` `rArr CB+5=2GBrArr CB =5=(1)/(sin theta)` From the EQ.(i), `AC=(2)/(sin theta) =2xx5 =10,00`. |
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