# ​ 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. ​

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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.

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O’ is the centre of the circle.

Chords AB = CD

OM ⊥ AB; ON ⊥ CD

In ΔOMB and ΔONC

BM = CN

∠OMB = ∠ONC [ ∵90° each]

∴ ΔOMB ≅ ΔONC [R.H.S congruence]

∴ OM = ON (CPCT)