If two equal chor

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)

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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