SSC CGL 2025 PYQ — Question 53

The correct answer is option 4 i.e. $\frac{x^2}{y^2} = \frac{125}{147}$.

AE : EB = 2 : 3

Let AE = 2k, EB = 3k

AB = 5k = x

CE : ED = 5 : 2

Let CE = 5m, ED = 2m

CD = 7m = y

By the intersecting chords theorem: AE × EB = CE × ED

(2k) × (3k) = (5m) × (2m)

⇒ 6k² = 10m²

⇒ 3k² = 5m²

⇒ k² = (5/3)m²

x² = (5k)² = 25k² = 25 × (5/3)m² = (125/3)m²

y² = (7m)² = 49m²

x²/y² = [(125/3)m²]/(49m²) = 125/147