ee1e8abd87
* feat(tools): add seed/solution restore script * chore(curriculum): remove empty sections' markers * chore(curriculum): add seed + solution to Chinese * chore: remove old formatter * fix: update getChallenges parse translated challenges separately, without reference to the source * chore(curriculum): add dashedName to English * chore(curriculum): add dashedName to Chinese * refactor: remove unused challenge property 'name' * fix: relax dashedName requirement * fix: stray tag Remove stray `pre` tag from challenge file. Signed-off-by: nhcarrigan <nhcarrigan@gmail.com> Co-authored-by: nhcarrigan <nhcarrigan@gmail.com>
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id, title, challengeType, forumTopicId, dashedName
| id | title | challengeType | forumTopicId | dashedName |
|---|---|---|---|---|
| 5900f46e1000cf542c50ff80 | Problem 257: Angular Bisectors | 5 | 301905 | problem-257-angular-bisectors |
--description--
Given is an integer sided triangle ABC with sides a ≤ b ≤ c.
(AB = c, BC = a and AC = b).
The angular bisectors of the triangle intersect the sides at points E, F and G (see picture below).
The segments EF, EG and FG partition the triangle ABC into four smaller triangles: AEG, BFE, CGF and EFG. It can be proven that for each of these four triangles the ratio area(ABC)/area(subtriangle) is rational. However, there exist triangles for which some or all of these ratios are integral.
How many triangles ABC with perimeter≤100,000,000 exist so that the ratio area(ABC)/area(AEG) is integral?
--hints--
euler257() should return 139012411.
assert.strictEqual(euler257(), 139012411);
--seed--
--seed-contents--
function euler257() {
return true;
}
euler257();
--solutions--
// solution required