The sum of radius of circles is 119 cm and the difference between their area is 17204 sq. cm.  What is the radius (in cm) of the larger circle?

82.5

Sum of radius = r₁ + r₂ = 119                (r₁ > r₂) 

Difference in area = π r₁² - π r₂²

                 17204 = π (r₁ - r₂) (r₁ + r₂)

                 17204 = \(\frac{22}{7}\) × 119 × (r₁ - r₂)

⇒ (r₁ - r₂) = 46

⇒ (r₁ + r₂) = 119

Adding both, we get

⇒ 2 r₁ = 165

⇒    r₁ = 82.5