Question

In the given figure ab and BC are two chords of a circle whose Centre is O such that angle abc is equal to angle CBD if a b is equals to 6 cm and angle b is equal to 30 degree find the measure of BC and angle AOC

Answer 1

hope this helps u.......

Answer 2

Ans

Step-by-step explanation:

Given that angle ABO= angle CBO

Therefore angle ABO=CBO=30 DEGREE

Angle AOC=2 angle ABC (Angle subtended by the arc at the centre is twice that subtended on the remain part of the circle)

Therefore

Angle AOC=2*30

=60 DEGREE

Construction: draw a perpendicular line from centre to chord AC which meets it at M

In triangle ABM and CBM

AM=BM. Perpendicular from centre to chord bisects the chord)

Angle BMA= Angle BMC=90degree (by construction)

BM=BM (common)

Therefore

Triangle ABM is congruent to triangle CBM (SAS cong. rule)

AB=CB(cpct)

Given

AB=6cm

Therefore BC=6cm

Therefore

Angle AOC=60degree

And

CB=6cm

Hope it helped you!!!