1.0 KiB
1.0 KiB
id | title | challengeType | forumTopicId | dashedName |
---|---|---|---|---|
5900f5071000cf542c510018 | Problem 410: Circle and tangent line | 5 | 302079 | problem-410-circle-and-tangent-line |
--description--
Let C
be the circle with radius r
, x^2 + y^2 = r^2
. We choose two points P(a, b)
and Q(-a, c)
so that the line passing through P
and Q
is tangent to C
.
For example, the quadruplet (r, a, b, c) = (2, 6, 2, -7)
satisfies this property.
Let F(R, X)
be the number of the integer quadruplets (r, a, b, c)
with this property, and with 0 < r ≤ R
and 0 < a ≤ X
.
We can verify that F(1, 5) = 10
, F(2, 10) = 52
and F(10, 100) = 3384
.
Find F({10}^8, {10}^9) + F({10}^9, {10}^8)
.
--hints--
circleAndTangentLine()
should return 799999783589946600
.
assert.strictEqual(circleAndTangentLine(), 799999783589946600);
--seed--
--seed-contents--
function circleAndTangentLine() {
return true;
}
circleAndTangentLine();
--solutions--
// solution required