Question

if two equal chord of a circle intersect within the circle,prove that the segments of one one chord are equal to corresponding segments of other chord

Answer 1

➣ Given : Two equal chords of circle intersect within circle.

➣ To prove : Prove that segment of chord are equal to other chord.

➣ To construct : Join perpendicular bisectors OL and OM from centers.

➣ Proof : In ∆OLN and ∆OMN,

Since chords are equal that's why they will be equidistant from each other.

OL = OM

Since OL and OM are perpendicular bisectors.

∠OLN = ∠OMM ( 90° each )

and ON = ON ( Common )

Hence, by RHS congruency ∆OLN ≅ ∆OMN.

LN = MN ( c.p.c.t ) _(1)

Since AB = CD

½ AB = ½ CD => BL = DM _(2) and

AL = CM _(3)

By doing (3) - (1)

AL - LN = CM - MN

✪ AN = CN

Now by doing (2) + (1)

BL + LN = DM + MN

✪ BN = DN

➣ Q.E.D

Answer 2

Answer:

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