Answer:
r = 8
Explanation:
using Pythagoras' identity in right triangle AOB
the square on the hypotenuse is equal to the sum of the squares on the other two sides , that is
OB² = OA² + AB²
(r + 2)² = r² + 6² ← expand factor using FOIL
r² + 4r + 4 = r² + 36 ( subtract r² from both sides )
4r + 4 = 36 ( subtract 4 from both sides )
4r = 32 ( divide both sides by 4 )
r = 8