Question

if two equal chords of a circle intersect within the circle prove that the segments of one chord are equal to the corresponding segment of the chord​

Answer 1

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Answer 2

Step-by-step explanation:

Given:-AB and CD are chords intersecting at E

AB = CD

To Prove :- AE = DE

CE = BE

Construction:- OM _|_ AB

ON _|_ CD

Proof :- OM _|_ AB

ON _|_CD

So, AM =BM =1/2 AB.

DN = CN = 1/2 CD.

As,AB= CD

1/2 AB = 1/2 CD

AM = DN

MB = CN

In triangle OME & triangle

ONE

OME = ONE

OE = OE

OM = ON

OME congruent to ONE

ME =NE

adding AM + ME =DN +NE

AE = DE

subtraction BM - ME = CN - ME

BE = CE

therefore, AE = DE & BE -CE

HENCE PROVED.