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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 the segment of one chord are equal to corresponding segment of the other chord

Posted by Radheshyam Thakur 5 years, 1 month ago

CBSE > Class 09 > Mathematics

1 answers

Yogita Ingle 5 years, 1 month 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=90o

△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.

1Thank You

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CBSE > Class 09 > Mathematics