SOLUTION: Two chords of a circle are perpendicular and congruent, does one of them have a diameter?

Question 199732: Two chords of a circle are perpendicular and congruent, does one of them have a diameter?
Found 2 solutions by vleith, RAY100:
Answer by vleith(2983) (Show Source): You can put this solution on YOUR website!
they would both be diameters IF they intersect at their midpoints. But it easy to see that two chords could be the same length AND perpendicular but NOT a diameter IF they intersect somewhere other than their midpoints.
Make an circle.
Draw a chord that is 'far away' from the center of the circle.
Now see that you could take a chord of the same length and 'slide it' towards one end of the first chord.
Make it perpendicular and slide it down until the ends touch the circle.
Do those two chords meet the congruent and perpendicular requirements? Are they a diameter?
Answer by RAY100(1637) (Show Source): You can put this solution on YOUR website!
Very interesting question
Let's start with a rough sketch of a circle, now one chord, now another perpendicular chord that goes thru center.
This is the situation that answers your question, yes it can happen but it does not have to.
.
The principle that puts the second chord thru the center is,,,, it must be a perpendicular bisector. ALL perp bisectors go thru center, hence could be diameters.
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It is easy to take your sketch, and just slide the second chord to one side or the other. It does not go thru center, and is not a diameter. Your problem did not specify bisection.
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Another interesting construction, again draw a rough circle and one chord. Draw a second chord, perpendicular to first but located at an end of the first chord. NOW, if we connect the other ends of the chord, we have a triangle. But, a very special triangle, it is a right inscribed triangle, that divides the circle into two semicircles, and has the hypotenuse as the diameter.
Good luck with class

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