SSC CGL 26 Oct 2014 Shift 2 Paper

In Ds OAB and OCA,
OC = OA = OB = radii
2 ∠ OAB + ∠ AOB = 180°
2 ∠ OAC + ∠ AOC = 180°
∴ ∠ AOB + ∠ AOC
= 360° – 2 (∠ OAB + ∠ OAC)
= 360° – 2 × 90° = 180°
AB = AC
∴ ∠ AOB = 90°
∠ OAB = 45°
∴ sin OAB = $\frac{\mathit{O}\mathit{B}}{\mathit{A}\mathit{B}}$
⇒ sin 45° = $\frac{\mathit{O}\mathit{B}}{5\sqrt{2}}$
⇒ OB = $5\sqrt{2}$ . sin 45°
= 5 $\sqrt{2}$ × $\frac{1}{\sqrt{2}}$ = 5 cm.