SSC CGL 2025 PYQ — Question 52

The correct answer is option 2 i.e. $\sqrt{149}$ cm.

Length of chord , L = $2\sqrt{R^2 - d^2}$

⇒ 20 = $2\sqrt{R^2 - d_1^2}$   

⇒ ${R^2 - d_1^2}$ = 100      ....(i)

Also, 14 = $2\sqrt{R^2 - d_2^2}$

⇒ ${R^2 - d_2^2}$ = 49     ....(ii)

Given, d₂ - d₁ = 3

Now subtract (ii) from (i),  ${R^2 - d_1^2}$ - (${R^2 - d_2^2}$)  = 100 - 49

⇒ (d₂ - d₁)(d₂ + d₁) = 51

⇒ (d₂ + d₁) = 17

Now, d₂ = 10 and d₁ = 7

${R^2 - d_1^2}$ = 100

⇒ R² = 100 + 49

⇒ R = $\sqrt{149}$