Find a, b and c on the triangle?

By the Pythagorean Theorem, we have

c = √ [8^2 + 6^2]  = √100  = 10

And by similar triangles, we have

8 / 6   = [ a + 8 ] / 9       cross-multiply

72  = 6 [a + 8 ]

72  = 6a + 48    subtract 48 from both sides

24  = 6a    divide both sides by 6

4 = a

And by similar triangles, again, we have

8 / c   = [ a + 8 ]  /  [ b + c ]

8 / 10  = [ 4 + 8 ] / [ b + 10]   

4 / 5  = [ 12 ] / [ b + 10 ]      cross-multiply

4 [ b + 10 ] = 12 * 5

4b + 40  = 60    subtract 40 from both sides

4b  = 20      divide both sides by 4

b = 5

It looks like similarity in right triangles... 

a=4

c=10

b=5