In figure, $C N ⊥ A B, D M ⊥ A B$ and $C N = D M$ . Are $O C$ and $O D$ equal? Why?

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Solution

In $Δ O M D$ and $Δ O N C$
$∠ O M D = ∠ O N C$ (each $90^{0}$ )
$∠ M O D = ∠ N O C$ (vertically opposite angles)
and $C N = D M$ (given)
$Δ O M D = Δ O N C$ (by AAS property)
$O C = O D$ (by c.p.c.t)
Hence proved.

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