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What is minimum radius of circle given chord length?
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What is minimum radius of circle given chord length (Fig.)
I started by setup two line perpendicular to each other.
And find out some area of triangle , then find radius of circle from triangle inscribe in circle formula.
I don't know how this could be correct answer please give any advice for me.
Thank you in advance.
geometry circle
asked Aug 2 at 18:50
ABCDEFG user157844
37429
add a comment |Â
up vote
0
down vote
favorite
What is minimum radius of circle given chord length (Fig.)
I started by setup two line perpendicular to each other.
And find out some area of triangle , then find radius of circle from triangle inscribe in circle formula.
I don't know how this could be correct answer please give any advice for me.
Thank you in advance.
geometry circle
asked Aug 2 at 18:50
ABCDEFG user157844
37429
add a comment |Â
up vote
0
down vote
favorite
up vote
0
down vote
favorite
What is minimum radius of circle given chord length (Fig.)
I started by setup two line perpendicular to each other.
And find out some area of triangle , then find radius of circle from triangle inscribe in circle formula.
I don't know how this could be correct answer please give any advice for me.
Thank you in advance.
geometry circle
asked Aug 2 at 18:50
ABCDEFG user157844
37429
What is minimum radius of circle given chord length (Fig.)
I started by setup two line perpendicular to each other.
And find out some area of triangle , then find radius of circle from triangle inscribe in circle formula.
I don't know how this could be correct answer please give any advice for me.
Thank you in advance.
geometry circle
asked Aug 2 at 18:50
ABCDEFG user157844
37429
asked Aug 2 at 18:50
ABCDEFG user157844
37429
asked Aug 2 at 18:50
ABCDEFG user157844
37429
asked Aug 2 at 18:50
ABCDEFG user157844
37429
37429
add a comment |Â
add a comment |Â
1 Answer
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If you don't know anything else about the two line segments $AB$, $AC$, and $CD$ except their lengths, then the minimum radius will be half the length of $AB$ (which at its longest is a diameter of the circle).
So, $(1/2)(2+5) = 7/2.$
answered Aug 2 at 19:41
John
21.9k32346
1
We need to be a little careful here. Extending $overlineCD$ could possibly lead to a longer chord of the circle, and thus a larger minimum radius. Let's check: If the extension has length $x$, then the Power of a Point theorem says that $3x = 2cdot 5 = 10$, so that $x = 10/3$. Thus, the extended chord has length $3+10/3 = 19/3$, which is less than $7$, so your calculation works. (On the other hand, if we had, for instance, $|CD| = 1$, then its extended form would have had length $11$.)
– Blue
Aug 2 at 21:54
add a comment |Â
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
1
down vote
If you don't know anything else about the two line segments $AB$, $AC$, and $CD$ except their lengths, then the minimum radius will be half the length of $AB$ (which at its longest is a diameter of the circle).
So, $(1/2)(2+5) = 7/2.$
answered Aug 2 at 19:41
John
21.9k32346
1
We need to be a little careful here. Extending $overlineCD$ could possibly lead to a longer chord of the circle, and thus a larger minimum radius. Let's check: If the extension has length $x$, then the Power of a Point theorem says that $3x = 2cdot 5 = 10$, so that $x = 10/3$. Thus, the extended chord has length $3+10/3 = 19/3$, which is less than $7$, so your calculation works. (On the other hand, if we had, for instance, $|CD| = 1$, then its extended form would have had length $11$.)
– Blue
Aug 2 at 21:54
add a comment |Â
up vote
1
down vote
If you don't know anything else about the two line segments $AB$, $AC$, and $CD$ except their lengths, then the minimum radius will be half the length of $AB$ (which at its longest is a diameter of the circle).
So, $(1/2)(2+5) = 7/2.$
answered Aug 2 at 19:41
John
21.9k32346
1
We need to be a little careful here. Extending $overlineCD$ could possibly lead to a longer chord of the circle, and thus a larger minimum radius. Let's check: If the extension has length $x$, then the Power of a Point theorem says that $3x = 2cdot 5 = 10$, so that $x = 10/3$. Thus, the extended chord has length $3+10/3 = 19/3$, which is less than $7$, so your calculation works. (On the other hand, if we had, for instance, $|CD| = 1$, then its extended form would have had length $11$.)
– Blue
Aug 2 at 21:54
add a comment |Â
up vote
1
down vote
up vote
1
down vote
If you don't know anything else about the two line segments $AB$, $AC$, and $CD$ except their lengths, then the minimum radius will be half the length of $AB$ (which at its longest is a diameter of the circle).
So, $(1/2)(2+5) = 7/2.$
answered Aug 2 at 19:41
John
21.9k32346
If you don't know anything else about the two line segments $AB$, $AC$, and $CD$ except their lengths, then the minimum radius will be half the length of $AB$ (which at its longest is a diameter of the circle).
So, $(1/2)(2+5) = 7/2.$
answered Aug 2 at 19:41
John
21.9k32346
answered Aug 2 at 19:41
John
21.9k32346
answered Aug 2 at 19:41
John
21.9k32346
answered Aug 2 at 19:41
John
21.9k32346
21.9k32346
1
We need to be a little careful here. Extending $overlineCD$ could possibly lead to a longer chord of the circle, and thus a larger minimum radius. Let's check: If the extension has length $x$, then the Power of a Point theorem says that $3x = 2cdot 5 = 10$, so that $x = 10/3$. Thus, the extended chord has length $3+10/3 = 19/3$, which is less than $7$, so your calculation works. (On the other hand, if we had, for instance, $|CD| = 1$, then its extended form would have had length $11$.)
– Blue
Aug 2 at 21:54
add a comment |Â
1
We need to be a little careful here. Extending $overlineCD$ could possibly lead to a longer chord of the circle, and thus a larger minimum radius. Let's check: If the extension has length $x$, then the Power of a Point theorem says that $3x = 2cdot 5 = 10$, so that $x = 10/3$. Thus, the extended chord has length $3+10/3 = 19/3$, which is less than $7$, so your calculation works. (On the other hand, if we had, for instance, $|CD| = 1$, then its extended form would have had length $11$.)
– Blue
Aug 2 at 21:54
1
1
We need to be a little careful here. Extending $overlineCD$ could possibly lead to a longer chord of the circle, and thus a larger minimum radius. Let's check: If the extension has length $x$, then the Power of a Point theorem says that $3x = 2cdot 5 = 10$, so that $x = 10/3$. Thus, the extended chord has length $3+10/3 = 19/3$, which is less than $7$, so your calculation works. (On the other hand, if we had, for instance, $|CD| = 1$, then its extended form would have had length $11$.)
– Blue
Aug 2 at 21:54
We need to be a little careful here. Extending $overlineCD$ could possibly lead to a longer chord of the circle, and thus a larger minimum radius. Let's check: If the extension has length $x$, then the Power of a Point theorem says that $3x = 2cdot 5 = 10$, so that $x = 10/3$. Thus, the extended chord has length $3+10/3 = 19/3$, which is less than $7$, so your calculation works. (On the other hand, if we had, for instance, $|CD| = 1$, then its extended form would have had length $11$.)
– Blue
Aug 2 at 21:54
add a comment |Â
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