Question

AOC is a diameter of a circle.Arc AXB = 1/2 arc BYC.Find angle BOC.

Answer 1

semi circle AXB = 1/2 semicircle BYC

so,
180 - Ф/ 360 x 2λr= 1/2 x Ф/360 x 2λr

360 - 2Ф = Ф

3Ф= 360

Ф= 120 
so ∠BOC = 120 

Answer 2

Answer:

Step-by-step explanation:

Axc=1/2arc byc

Angle boa =boc/2-eq.1 (since if arcs are congruent so thir corresponding chords are also equal and if corresponding chords are equal so angles opp. To equal sides will also be equal)

Now,angle aoc =2 angle abc -eq.2( angle at centre is twice the angle at remaining part of the circle )

Now using ii

Angle aoc =2abc

boa+boc=2abc

Boc/2+boc =2abc (using i )

Boc +boc /2=2abc

Boc+2boc/2=2abc

Boc +2boc=4abc

3boc=4abc

Boc=4/3abc

Boc =4/3*1/2 aoc{using eq.2}

Boc=2/3*180(since aoc is a straight line therefore ist measure 180°)

Angle boc =120°ans.

Hope it works .....