BMAD Posted June 14, 2016 Report Share Posted June 14, 2016 (edited) How many circles exist with the following properties... 1. Contains two chords that are 2 cm from each other 2. The longer chord only gets as close as 1 cm from the center. 3. The shorter chord only gets as close as 3 cm from the center. versus How many circles exist with the following properties... 1. Contains two chords that only gets as close as 2 cm from each other. 2. The longer chord only gets as close as 1 cm from the center. 3. The shorter chord only gets as close as 3 cm from the center. Edited June 14, 2016 by BMAD Quote Link to comment Share on other sites More sharing options...
0 BMAD Posted June 14, 2016 Author Report Share Posted June 14, 2016 (edited) 1 hour ago, BMAD said: How many circles exist with the following properties... 1. Contains two chords that are 2 cm from each other 2. The longer chord only gets as close as 1 cm from the center. 3. The shorter chord only gets as close as 3 cm from the center. versus How many circles exist with the following properties... 1. Contains two chords that only gets as close as 2 cm from each other. 2. The longer chord only gets as close as 1 cm from the center. 3. The shorter chord only gets as close as 3 cm from the center. I forgot, say the smaller chord is 5 cm in length and the bigger chord 7 cm in length Edited June 14, 2016 by BMAD Quote Link to comment Share on other sites More sharing options...
0 bonanova Posted June 15, 2016 Report Share Posted June 15, 2016 Spoiler A circle that has a chord of length of 2c that gets as close as r to its center has a radius of sqrt( r 2 + c 2). A circle with a 7cm chord that gets as close as 1cm to its center has a radius of 3.640 cm (red circle) A circle with a 5cm chord that gets as close as 3cm to its center has a radius of 3.905 cm (blue circle) Since these are different circles, the answer to both questions is zero. The green circles have radii (distances from center) of 1 and 3, and the chords have lengths 7 and 5, respectively If the chords are not parallel, their distance becomes less than 2 cm. Quote Link to comment Share on other sites More sharing options...
0 BMAD Posted June 15, 2016 Author Report Share Posted June 15, 2016 4 hours ago, bonanova said: Hide contents A circle that has a chord of length of 2c that gets as close as r to its center has a radius of sqrt( r 2 + c 2). A circle with a 7cm chord that gets as close as 1cm to its center has a radius of 3.640 cm (red circle) A circle with a 5cm chord that gets as close as 3cm to its center has a radius of 3.905 cm (blue circle) Since these are different circles, the answer to both questions is zero. The green circles have radii (distances from center) of 1 and 3, and the chords have lengths 7 and 5, respectively If the chords are not parallel, their distance becomes less than 2 cm. I disagree with your conclusion in the second case. Quote Link to comment Share on other sites More sharing options...
0 bonanova Posted June 17, 2016 Report Share Posted June 17, 2016 On 6/15/2016 at 8:27 AM, BMAD said: I disagree with your conclusion in the second case. The conclusion that they must be parallel? Quote Link to comment Share on other sites More sharing options...
0 BMAD Posted June 17, 2016 Author Report Share Posted June 17, 2016 3 hours ago, bonanova said: The conclusion that they must be parallel? i disagree with this line: If the chords are not parallel, their distance becomes less than 2 cm. Quote Link to comment Share on other sites More sharing options...
0 bonanova Posted June 23, 2016 Report Share Posted June 23, 2016 On 6/17/2016 at 11:00 AM, BMAD said: i disagree with this line: If the chords are not parallel, their distance becomes less than 2 cm. Of course you're right. I needlessly put the chords on the same side of center. Quote Link to comment Share on other sites More sharing options...
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BMAD
How many circles exist with the following properties...
1. Contains two chords that are 2 cm from each other
2. The longer chord only gets as close as 1 cm from the center.
3. The shorter chord only gets as close as 3 cm from the center.
versus
How many circles exist with the following properties...
1. Contains two chords that only gets as close as 2 cm from each other.
2. The longer chord only gets as close as 1 cm from the center.
3. The shorter chord only gets as close as 3 cm from the center.
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