Question

in the given figure o is the centre of the circle. if arc ac = arc aband bc is the angle bisector of angle abo prove that abo is an equilateral triangle​

Answer 1

Answer:

Here, △ABC is an equilateral triangle inscribed in a circle with centre O.

⇒AB=AC=BC [∵△ABC is equilateral]

∠AOB=∠AOC=∠BOC [equal chords subtend equal angles at centre]

⇒∠AOB=∠AOC...i)

Now, ∠AOB and ∠APB are angles subtended by an arc AB at centre and at remaining part of the circle by same arc.

Therefore, ∠APB=

2

∠AOB

...ii)

Similarly, ∠APC=

2

∠AOC

...iii)

Using (i),(ii) and (iii), we have

∠APB=∠APC

Hence, PA is angle bisector of ∠BPC