I am usually pretty good about interpreting what a question is asking when it is in the form, "prove that if p, then q," where p and q are statements. However, I cannot seem to understand how to interpret when it is in the form "prove that p if and only if q." The statement I am working with currently is this: "Prove that a radius of a circle is perpendicular to a chord if and only if the chord is bisected by the radius. Assume the chord is not the diameter of the circle."(adsbygoogle = window.adsbygoogle || []).push({});

How do I begin proving this? What I mean is how can I decompose this proposition to clearer propositions that can be proved individually? I looked online and I couldn't find much about iff statements, so help would be appreciated.

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# I Proving propositions involving "if and only if"

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