Question

In the adjoining figure,AB and BC are two equal chords of a circle with center O. if OM bisector AB, ON bisector BC is joined,prove that.
(I) triangle OMB contribute ONB and
(ii)ON bisect triangle ABC​

Answer 1

Answer:

Step-by-step explanation: ANSWER

(i) True, equal chords are equidistant from the centre .

(ii) True, In △  

′

sOMB and ONB,

OM=ON(Proved in (i))

OB=BO(Common)

∠OMB=∠ONB=90  

∘

 

therefore△OMB≅△ONB(RHS)

(iii)△OMB≅△ONB⇒∠OBM=∠OBN(cpct)

⇒BObisects∠ABC

Hence, all the statements are true statements  

hope this was useful

Answer 2

i)in /_\ OMB& /_\ONB,

/_OMB=/_ONB (right angles)

MB=NB (bisected chord)

OB=OB (common)

therefore, /_\ OMB=~/_\ONB,

ii)/_mbo=/_obn(CPCT)

/_mbo+/_obn=/_abc

hence proven