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Options

A. are such that the number of common tangents on them is 2
B. are orthogonal
C. are such that the length of their common tangent is `5(12//5)^(1//4)`
D. are such that the length of their common chord is `5sqrt(3//2)`

Answer

1,2,3,4

Explanation

`r_(1)=5,r_(2)=sqrt(15),C_(1)C_(2)=sqrt(40)`
`:. r_(1)+r_(2) gt C_(1)C_(2)gt r_(1)-r_(2)`
Hence, the circles intersect at two distinct points.
There are two common tangents. Also,
`2g_(1)g_(2)+2f_(1)f_(2)=2(1)(3)+2(2)(-4)= -10`
and `c_(1)+c_(2)= -20+10 = -10`
Thus, the two circles are orthogonal.
Length of common chord `=(2r_(1)r_(2))/(sqrt(r_(1)^(2)+r_(1)^(2))) = 5 sqrt((3)/(2))`
Length of common tangent `=sqrt(C_(1)C_(2)^(2)-(r_(1)-r_(2))^(2))=5 ((12)/(5))^(1//4)`