Question

AHHHHH! IM FREAKING OUT I NEED HELP NOW AND I WILL MARK BRAINLEST!!!! Question :
What is the length of the common tangent between two non-intersecting circles with radii r and 3r, having the shortest distance between them equal to the radius of the first circle?

Answer 1

Answer:

Step-by-step explanation:

if i can draw, then i can explain better

distance between centers=r+3r=4r

we have to find the side of a right angled triangle by pythagoras theorem

given hypotenuse=4r

and one side=3r-r=2r

$d=\sqrt{(4r)^2-(2r)^2} =\sqrt{12r^2}=2\sqrt{3}r$

this is the distance if they touch.

but if they are r distance apart

then distance between centers=r+r+3r=5r

so hypotenuse=5r

length of tangent

$=\sqrt{(5r)^2-(2r)^2} \\=\sqrt{21r^2} \\=\sqrt{21} r$