A) \[\left( \frac{20}{3},\frac{5}{3} \right)\]
B) \[(5,2)\]
C) \[(4,3)\]
D) \[\left( \frac{14}{3},\frac{7}{3} \right)\]
Correct Answer: A
Solution :
AD is the angle bisector of\[\angle BAC\]. So, by the angle bisector theorem in \[\Delta ABC,\]we have \[\frac{AB}{AC}=\frac{BD}{DC}\] ?..(i) Now, \[AB=5\]and \[AC=10\] \[\therefore \] \[\frac{1}{2}=\frac{BD}{DC}\] [using (i)] Thus, D divides BC in the ratio\[1:2\]. \[\therefore \] \[D=\left( \frac{2\times 6+1\times 8}{2+1},\,\frac{-2\times 2+9\times 1}{2+1} \right)=\left( \frac{20}{3},\frac{5}{3} \right)\]You need to login to perform this action.
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