Two chords AB and CO of a circle with center O, intersect each other at P. If ∠AOD = 120° and ∠BOC = 80°, then the value of ∠APC is ?
Answer & explanation
Correct answer: option 3
∠AOD = 120°
⇒ ∠ACD = \(\frac{1}{2}\) ∠AOD = \(\frac{1}{2}\) (120°) = 60° [angle made by chord AD at circumference]
∠BOC = 80°
⇒ ∠BAC = 40° [angle made by chord BC at circumference)
Now, in ΔAPC
⇒ ∠ACP + ∠APC + ∠CAP = 180°
⇒ 60° + ∠APC + 40° = 180°
⇒ ∠APC = 80°