Question

# The length of the direct common tangent of the circles $$x^{2}+y^{2}-4x-10y+28=0$$ and $$x^{2}+y^{2}+4x-6y+4=0$$ is

A
2
B
4
C
11
D
16

Solution

## The correct option is A $$\sqrt{11}$$ From point (12)length of direct common tangent $$=\sqrt{d^{2}-(r_{1}-r_{2})^{2}}$$distance between centres $$d=\sqrt{(4)^{2}+(2)^{2}}$$$$=\sqrt{20}$$and $$r_{1}=1$$ and $$r_{2}=4$$$$\therefore L=\sqrt{20-(3)^{2}}$$$$L=\sqrt{11}$$Maths

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