Q. 104.3( 6 Votes )

If two equal chor

Answer :


Let AB and CD be two equal chords of a circle which are intersecting at a point E.


Construction:


Draw OF and OG perpendiculars on the chords


Join OE.


Consider ΔOFE and ΔOGE,


OF = OG [Equal chords]


⇒∠OFE = OGE [Each 90°]


OE = OE [Common]


By RHS congruence rule,


ΔOFE ΔOGE


By CPCT,


FE = GE … (1)


Given AB = CD … (2)


1/2 AB = 1/2 CD


AG = CF … (3)


Adding equations (1) and (3),


AG + GE = CF + FE


AE = CE … (4)


Subtracting equation (4) from (2),


AB – AE = CD - CE


BE = DE … (5)


From (4) and (5),


We can see that two parts of one chord are equal to two parts of another chord.


Hence proved


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