Question

please give me this answer correctly ​

Answer 1

Answer:

A galaxy is a huge collection of gas, dust, and billions of stars and their solar systems, all held together by gravity. We live on a planet called Earth that is part of our solar system. ... A galaxy is a huge collection of gas, dust, and billions of stars and their solar systems

Answer 2

Let a, b and c be the radii of the three circles. We first draw the lines AA', BB' and CC' perpendicular to line L. B'C, CA' and BA" are parallel to line L.

three tangent circles solution

Let x = B'C, y=A'C and z = BA". Pythagora's theorem applied to the right triangle BCB' gives

x 2 + BB' 2 = BC 2

Note that BB' = b - c and BC = b + c. The above equation may be written as follows

x 2 + (b - c) 2 = (b + c) 2

Expand the above, group like terms and solve for x

x 2 = 4 b c

x = 2 Square Root( b c )

Use Pythagora's theorem to triangle AA'C to obtain

y 2 + (a - c) 2 = (a + c) 2

Expand, group like terms and solve for y

y 2 = 4 a c

y = 2 Square Root( a c )

Use Pythagora's theorem to triangle AA"B to obtain

z 2 + (a - b) 2 = (a + b) 2

Expand, group and solve for z