Question

If two equal chords of a circle intersect
within the circle , prove that the segme-
nts of one chord are equal to the
corrosponding segments of the other
chord .​

Answer 1

Answer:

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Answer 2

Step-by-step explanation:

GIVEN: AB and CD are chords of a circke with centre O. AB and CD intersect at P and AB=CD.

TO PROVE: a) AP = PD b) PB = CP

CONSTRUCTION : draw OM | AB, ON | CD.

PROOF: AM = MB = I/2AB

CN = ND = 1/2CD

AM = ND and MB = CN.........(1)

In triangle OMP and ONP, we have

OM = AN

angle OMP = angle ONP ( 90°)

OP = OP ( common)

Thus by RHS,

Triangle OMP ~= triangle ONP

MP = PN.........(2)

Adding eq. 1 and 2

AM+MP=ND+PN

AP=PD

subtracting eq.2 from 1

MB - MP = CN - PN

PB = CP

hence, proved