In figure, OP and OQ bisects ∠BOC and ∠AOC respectively. Prove tha

1.	In figure, OP and OQ bisects ∠BOC and ∠AOC respectively. Prove that ∠POQ = 900 .
Answer» ∴ OP bisects ∠BOC ∴ ∠POC = 1/2 ∠BOC ...(i) Also OQ bisects ∠AOC ∴ ∠COQ = 1/2 ∠AOC ...(ii) ∴ OC stands on AB ∴ ∠AOC + ∠BOC = 180⁰ [Linear pair] ⇒ 1/2 ∠AOC + 1/2 ∠BOC = 1/2 × 180⁰ ⇒ ∠COQ + ∠POC = 90⁰ [Using (i) & (ii)] ⇒ ∠POQ = 90⁰ [By angle sum property]

In figure, OP and OQ bisects ∠BOC and ∠AOC respectively. Prove that ∠POQ = 900 .

Answer»

∴ OP bisects ∠BOC

∴ ∠POC = 1/2 ∠BOC ...(i)

Also OQ bisects ∠AOC

∴ ∠COQ = 1/2 ∠AOC ...(ii)

∴ OC stands on AB

∴ ∠AOC + ∠BOC = 180⁰ [Linear pair]

⇒ 1/2 ∠AOC + 1/2 ∠BOC = 1/2 × 180⁰

⇒ ∠COQ + ∠POC = 90⁰ [Using (i) & (ii)]

⇒ ∠POQ = 90⁰ [By angle sum property]