Question

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

Answer 1

Answer:

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