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) On 6/14/2016 at 2:43 PM, 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. Expand 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 Reveal hidden 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. Quote Link to comment Share on other sites More sharing options...
0 BMAD Posted June 15, 2016 Author Report Share Posted June 15, 2016 On 6/15/2016 at 8:18 AM, bonanova said: Reveal hidden 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. Expand 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 12:27 PM, BMAD said: I disagree with your conclusion in the second case. Expand 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 On 6/17/2016 at 12:09 PM, bonanova said: The conclusion that they must be parallel? Expand 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 3:00 PM, BMAD said: i disagree with this line: If the chords are not parallel, their distance becomes less than 2 cm. Expand 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...
Question
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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