1.5 KiB
1.5 KiB
id | title | challengeType | forumTopicId | dashedName |
---|---|---|---|---|
5900f4751000cf542c50ff87 | Problem 264: Triangle Centres | 5 | 301913 | problem-264-triangle-centres |
--description--
Consider all the triangles having:
- All their vertices on lattice points.
- Circumcentre at the origin O.
- Orthocentre at the point H(5, 0).
There are nine such triangles having a \text{perimeter} ≤ 50
.
Listed and shown in ascending order of their perimeter, they are:
A(-4, 3), B(5, 0), C(4, -3) A(4, 3), B(5, 0), C(-4, -3) A(-3, 4), B(5, 0), C(3, -4) A(3, 4), B(5, 0), C(-3, -4) A(0, 5), B(5, 0), C(0, -5) A(1, 8), B(8, -1), C(-4, -7) A(8, 1), B(1, -8), C(-4, 7) A(2, 9), B(9, -2), C(-6, -7) A(9, 2), B(2, -9), C(-6, 7) |
The sum of their perimeters, rounded to four decimal places, is 291.0089.
Find all such triangles with a \text{perimeter} ≤ {10}^5
. Enter as your answer the sum of their perimeters rounded to four decimal places.
--hints--
triangleCentres()
should return 2816417.1055
.
assert.strictEqual(triangleCentres(), 2816417.1055);
--seed--
--seed-contents--
function triangleCentres() {
return true;
}
triangleCentres();
--solutions--
// solution required