Mathematics
Show that equal chords of a circle subtend equal angles at the centre of the circle.
Circles
3 Likes
Answer
Given: AB and CD are two equal chords of a circle with center O.
In Δ AOB and Δ COD,
OA = OC (Radii of a circle)
OB = OD (Radii of a circle)
AB = CD (Given)
By SSS congruency criterion,
Δ AOB ≅ Δ COD
∴ ∠AOB = ∠COD (By C.P.C.T.C.)
Hence, equal chords of a circle subtend equal angles at the centre.
Answered By
1 Like
Related Questions
If a diameter of a circle bisects each of the two chords of a circle, then prove that the chords are parallel.
If two chords of a circle are equally inclined to the diameter through their point of intersection, prove that the chords are equal.
In the given figure, equal chords AB and CD of a circle with centre O cut at right angles at P. If L and M are mid-points of AB and CD respectively, prove that OLPM is a square.
Prove that the perpendicular bisector of a chord of a circle always passes through the centre.
