Question

Prove that equal chords of a circle are equidistant from the centre.​

Answer 1

Answer:

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Answer 2

Answer:-

★ Given:-

▪︎O is the center of circle

▪︎Two equal chords AB = CD

▪︎OM ⊥ AB and ON ⊥ CD

★ To Prove:-

• OM = ON

★ Construction:-

• Join OA

• Join OC

★ Proof:-

AB = CD [ Given ]

½AB = ½CD [ half of given ]

According to theoream line Perpendicular from the centre to the chord bisects the chord

AM = CN ---- Equation 1

In ∆ OMA and ∆ ONC

OA = OC ( Each equal to radii )

∠ OMA = ∠ ONC ( Each 90° )

AM = CN ( From equation 1 )

∆ OMA ≅ ∆ ONC [ R.H.S. congruence rule ]

∴ OM = CN ( C.P.C.T. )

Hence, Proved.