Answer:
r = 7
Step-by-step explanation:
The angle between the tangent ST and the radius QS at the point of contact is 90° , then
Δ QST is right
Using Pythagoras' identity in the right triangle
(r + 18)² = r² + 24² , that is
r² + 36r + 324 = r² + 576 ( subtract r² from both sides )
36r + 324 = 576 ( subtract 324 from both sides )
36r = 252 ( divide both sides by 36 )
r = 7
