A triangle with three cevians
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The figure to the right shows a triangle with three cevians drawn through an interior point, and all perimeter segment lengths are given in meters. What is the value of s?
I'm not sure if there is any significance in all three ceva meeting at one point within the triangle... I feel like there might be, but I don't see how to utilise this fact.
I thought using heron's formula and then comparing it to another way of getting the triangle's area. However, I'm not sure how I can get the triangle's area the second (unknown) way.
Perhaps I could use triangle inequality, but that doesn't seem to get me very far, either.
How can I solve this?
geometry contest-math euclidean-geometry triangle
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up vote
0
down vote
favorite
The figure to the right shows a triangle with three cevians drawn through an interior point, and all perimeter segment lengths are given in meters. What is the value of s?
I'm not sure if there is any significance in all three ceva meeting at one point within the triangle... I feel like there might be, but I don't see how to utilise this fact.
I thought using heron's formula and then comparing it to another way of getting the triangle's area. However, I'm not sure how I can get the triangle's area the second (unknown) way.
Perhaps I could use triangle inequality, but that doesn't seem to get me very far, either.
How can I solve this?
geometry contest-math euclidean-geometry triangle
add a comment |Â
up vote
0
down vote
favorite
up vote
0
down vote
favorite
The figure to the right shows a triangle with three cevians drawn through an interior point, and all perimeter segment lengths are given in meters. What is the value of s?
I'm not sure if there is any significance in all three ceva meeting at one point within the triangle... I feel like there might be, but I don't see how to utilise this fact.
I thought using heron's formula and then comparing it to another way of getting the triangle's area. However, I'm not sure how I can get the triangle's area the second (unknown) way.
Perhaps I could use triangle inequality, but that doesn't seem to get me very far, either.
How can I solve this?
geometry contest-math euclidean-geometry triangle
The figure to the right shows a triangle with three cevians drawn through an interior point, and all perimeter segment lengths are given in meters. What is the value of s?
I'm not sure if there is any significance in all three ceva meeting at one point within the triangle... I feel like there might be, but I don't see how to utilise this fact.
I thought using heron's formula and then comparing it to another way of getting the triangle's area. However, I'm not sure how I can get the triangle's area the second (unknown) way.
Perhaps I could use triangle inequality, but that doesn't seem to get me very far, either.
How can I solve this?
geometry contest-math euclidean-geometry triangle
edited Aug 26 at 13:34
greedoid
27.9k93776
27.9k93776
asked Aug 26 at 13:10
jjhh
2,0291918
2,0291918
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add a comment |Â
1 Answer
1
active
oldest
votes
up vote
2
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accepted
Do you know Ceva's theorem? Acording to that theorem we have:
$$sover 5cdot 4over 3cdot 4over 2=1$$
so...
add a comment |Â
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
2
down vote
accepted
Do you know Ceva's theorem? Acording to that theorem we have:
$$sover 5cdot 4over 3cdot 4over 2=1$$
so...
add a comment |Â
up vote
2
down vote
accepted
Do you know Ceva's theorem? Acording to that theorem we have:
$$sover 5cdot 4over 3cdot 4over 2=1$$
so...
add a comment |Â
up vote
2
down vote
accepted
up vote
2
down vote
accepted
Do you know Ceva's theorem? Acording to that theorem we have:
$$sover 5cdot 4over 3cdot 4over 2=1$$
so...
Do you know Ceva's theorem? Acording to that theorem we have:
$$sover 5cdot 4over 3cdot 4over 2=1$$
so...
answered Aug 26 at 13:33
greedoid
27.9k93776
27.9k93776
add a comment |Â
add a comment |Â
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