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  1. #1
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    Question circle problem please help

    AB and CD are two chords of a circle intersecting each other at P such that AP = CP. show that AB = CD
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  2. #2
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    Quote Originally Posted by saha.subham View Post
    AB and CD are two chords of a circle intersecting each other at P such that AP = CP. show that AB = CD
    (1) AP=CP..........................................Given

    (2) AP \cdot PB = CP \cdot PD.............................When chords intersect in a circle, the product of their segments is equal.

    (3)  PB = PD..........................................Division (AP=CP)

    (4)  AP+PB = CP+PD...........................Addition (1) and (3)

    (5) AP+PB=AB \ \ and \ \ CP+PD=CD.......Segment Addition Postulate

    (6) AB=CD..........................................Substitu tion (4) and (5)
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