A circle with center O has radius 8 units and circle P has radius 3 units. The circles are externally tangent to each other at point Q. Segment TS is the common external tangent to circle O and circle P at points T and S, respectively. What is the length of segment OS? Express your answer in simplest radical form.
+128406 See the following :
Let the circle with a radius of 8 be centered at the origin
Let the circle with the radius of 3 be centered at P = ( a , -5)
The centers of the circles will be 11 units apart
And we can use a right triangle with a hypotenuse of 11 = OP and one leg of 5 = RP .....to find a = OR we have
sqry [ 11^2 - 5^2] = sqrt [96] = 6sqrt (4) = OR = a
O = (0,0) S = ( 4√6 , -8 ) = ( √ 96, -8)
So OS =sqrt [ (√96)^2 + (-8)^2 ] = sqrt [ 96 + 64 ] = sqrt [ 160 ] = 4 sqrt (10)
