Question

ABC is a cyclic equilateral triangle p is the point on the arc of PC the circle opposite to the vertex A.Prove that PA=PB+PC with geometry figire​

Answer 1

Step-by-step explanation:

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.

solution