Question

In the figure given O is the centre of the circle. Find x + y + z.​

Answer 1

Answer:

a) Given:

O is the centre of the circle.

To Prove : ∠AOC=2(∠ACB+∠BAC).

Proof:

In △ABC,∠ACB+∠BAC+∠ABC=180°(Sum of angles of a triangle)

⇒∠ABC=180

o

−(∠ACB+∠BAC)..(i)

In the circle, arc AC subtends ∠AOC at the centre and ∠ABC at the remaining part of the circle.

∴ reflex∠AOC=2∠ABC…(ii)

⇒ reflex∠AOC=2{(180

o

−(∠ACB+∠BAC)}

⇒ reflex∠AOC=360

o

−2(∠ACB+∠BAC)

But ∠AOC=360

o

−reflex ∠AOC

=360−(360

o

−2(∠ACB+∠BAC)

=360

o

−360

o

+2(∠ACB+∠BAC)

=2(∠ACB+∠BAC)

Hence ∠AOC=2(∠ACB+∠BAC)

mark it Braillent