# Prove that equal Given: AB = CD

Construction: Drop perpendiculars OX and OY on to AB and CD respectively and join OA and OD.

Here, OX AB (perpendicular from center to chord divides it into two equal halves)

AX = BX = – – (1)

OY CD (perpendicular from center to chords divides it into equal halves

CY = DY = – – (2)

Now, given that

AB = CD = AX = DY (from –1 and –2 ) – – (3)

In ΔAOX and ΔDOY

OXA = OYD (right angle)

AX = DY (from –3 )

BY RHS congruency

ΔAOX ΔDOY

OX = OY (by C.P.C.T)

Hence proved.

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