Prove that equal chords of a circle subtend equal angles at the centre
Answers
Answered by
1
make two chords of equal length
prove them congruent by sss creteria
then by cpct prove that angle subtended by the two chords at center are equal
prove them congruent by sss creteria
then by cpct prove that angle subtended by the two chords at center are equal
Answered by
6
Statement : Equal chords of a circle subtend equal angles at the centre.
Given : AB and CD are chords of a circle with centre O, such that AB = CD.
To prove : ∠AOC = ∠COD
Proof :
In ΔAOB and ΔCOD,
AO = CO [radii of same circle]
BO = DO [radii of same circle]
AB = CD [given]
ΔAOB ≅ ΔCOD [SSS]
∠AOB = ∠COD [C. P. C. T]
Hence, Equal chords of a circle subtend equal angles at the centre.
Given : AB and CD are chords of a circle with centre O, such that AB = CD.
To prove : ∠AOC = ∠COD
Proof :
In ΔAOB and ΔCOD,
AO = CO [radii of same circle]
BO = DO [radii of same circle]
AB = CD [given]
ΔAOB ≅ ΔCOD [SSS]
∠AOB = ∠COD [C. P. C. T]
Hence, Equal chords of a circle subtend equal angles at the centre.
Attachments:
Similar questions