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If two equal chords of a …

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If two equal chords of a circle intersect within the circle prove that thesegments of one chord are equal to corresponding segments of the other chord

Posted by Ashish Kumar 3 years, 8 months ago

CBSE > Class 09 > Mathematics

1 answers

Alphonsa Jimmy 3 years, 8 months ago

Drop a perpendicular from O to both chords AB and CD In △OMP and △ONP As chords are equal, perpendicular from centre would also be equal. OM=ON OP is common. ∠OMP=∠ONP=90 o △OMP ≅ △ONP (RHS Congruence) PM=PN ......................(1) AM=BM (Perpendicular from centre bisects the chord) Similarly ,CN=DN As AB=CD AB−AM=CD−DN BM=CN .........................(2) From (1) and (2) BM−PM=CN−PN PB=PC AM=DN (Half the length of equal chords are equal) AM+PM=DN+PN AP=PD Therefore , PB=PC and AP=PD is proved.

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