Draw a circle O of any radius. Draw each of the following in it :
a) Minor arc AB
b) Central angle COD
c) Inscribed angles CAD AND CBD
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Sol: We have a circle having its centre at O and two equal chords AB and CD such that they subtend ∠AOB and ∠COD respectively at the centre, i.e. at O.
We have to prove that
∠AOB = ∠COD
Now, in ΔAOB and ΔCOD, we have
AO = CO [Radii of the same circle]
BO = DO [Radii of the same circle]
AB = CD [Given]
∴ ΔAOB &becong; ΔCOD [SAS criterion]
∴Their correspondong parts are equal
∴ ∠AOB = ∠COD
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