If two chords AB and AC of a circle with centre O are such that the centre O lies on the bisector of angle BAC, then prove that AB=AC
Answers
AB = AC if If two chords AB and AC of a circle with centre O are such that the centre O lies on the bisector of angle BAC
Step-by-step explanation:
If two chords AB and AC of a circle with centre O are such that the centre O lies on the bisector of angle BAC
=> ∠BAO = ∠CAO = (1/2)∠BAC
Now join OB & OC
compare Δ OAB & OAC
OB = OC ( Radius)
OA = OA ( common side)
∠BAO = ∠CAO
=> Δ OAB ≅ OAC
=> AB = AC
QED
Proved
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Answer:
Step-by-step explanation:
If two chords AB and AC of a circle with centre O are such that the centre O lies on the bisector of angle BAC
=> ∠BAO = ∠CAO = (1/2)∠BAC
Now join OB & OC
compare Δ OAB & OAC
OB = OC ( Radius)
OA = OA ( common side)
∠BAO = ∠CAO
=> Δ OAB ≅ OAC
=> AB = AC
QED
Proved.
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