SSC CGL 2021 PYQ — Question 62

The correct answer is option 2 i.e. 3√13

Given :

AB = 12 cm , CD = 18 cm

Distance between the chords AB and CD is 3 cm

Calculations :

OP is perpendicular drawn from centre and OB is radius

AP = PB = 12/2 = 6 cm

ΔPOB, using pythagoras theorem,

⇒ OB² = PB² + OP²

⇒ OB² = 6² + OP²

Similarly for chord CD

⇒ CQ = QD = 18/2 = 9 cm

In ΔQDC,

⇒ OD² = QD² + OQ² 

⇒ OD² = 9² + OQ² 

Then, OP = OQ + QP

⇒ OP = OQ + 3

OD = OB (Radii of the circle)

⇒ 6² + OP² = 9² + OQ²

⇒ (OQ + 3)² - OQ² = 45

⇒ OQ² + 9 + 6OQ - OQ² = 45

⇒ 9 + 6OQ = 45

⇒ 6OQ =36

⇒ OQ = 6 cm

Then, OD² = 9² + 6² = 117

⇒ OD = $\sqrt{117}$ = $3\sqrt{13}$ cm