​ In the figure, O is the centre of the circle and AB = CD. OM is perpendicular on AB and ON is perpendicular on CD . Then prove that OM = ON. ​

Question

In the figure, O is the centre of the circle and AB = CD. OM is perpendicular on \(\overline {AB}\) and \(\overline {ON}\) is perpendicular on \(\overline {CD}\) . Then prove that OM = ON.

Answer 1

O’ is the centre of the circle.

Chords AB = CD 

OM ⊥ AB; ON ⊥ CD 

In ΔOMB and ΔONC 

OB = OC [∵ radii]

BM = CN 

∠OMB = ∠ONC [ ∵90° each] 

∴ ΔOMB ≅ ΔONC [R.H.S congruence] 

∴ OM = ON (CPCT)