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Thread: circle problem please help

  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) $\displaystyle AP=CP$..........................................Given

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

    (3) $\displaystyle PB = PD$..........................................Division (AP=CP)

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

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

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