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In the given figure, ‘O’ is the centre of the circle and AB, CD are equal chords. If ∠AOB = 70°. Find the angles of ΔOCD.

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‘O’ is the centre of the circle. 

AB, CD are equal chords 

⇒ They subtend equal angles at the centre. 

∴ ∠AOB =∠COD = 70° 

Now in ΔOCD 

∠OCD = ∠ODC [∵ OC = OD; radii angles opp. to equal sides] 

∴ ∠OCD + ∠ODC + 70° = 180° 

= ∠OCD +∠ODC = 180° – 70° = 110° 

∴ ∠OCD + ∠ODC = 110° = 55°

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