Chords that are equidistant from the center of the circle

Asked by admin @ 04/08/2021 in Math viewed by 278 People

Chords equidistant from the centre of the circle are equal in length

Answered by admin @ 04/08/2021

To Prove: AB = CD

Construction: Join OA and OC.

Proof:

OL ⊥ AB

⇒AL = BL [ Since, the ⊥cular from the centre of a circle to a chord bisects the chord ]

and, OM ⊥ CD

⇒ CM = DM [ Since, the ⊥cular from the centre of a circle to a chord bisects the chord

=> OA=OC (Common hypotenuse)

Therefore..♢ALO ~= ♢CMO( SSS rule)

NOW....AL=CM (C.P.C.T)

AND 2AL=2 CM

Therefore..AB=CD (Hence, Proved)
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