A regular hexagon has vertices A, B, C, D, E and F (labelled anticlockwise).
Vertices A and D have coordinates A (9, 11) and D (1, 1).
Find OB, the exact distance from the origin to vertex B.
The distance from A to D is 10√2.
The side length of the hexagon is 5√2
The vector from A to D is of angle 225 degrees.
The vector from A to B is 60 degrees less than that: 165 degrees.
tan(165*pi/180) = 0.267949192431123 which is the slope of segment AB
A is at (9, 11)
B is at (s, t) with s<9 and t>11
(11t)/(9s) = 0.267949192431123
and
(9s)^2 + (11t)^2 = 50
(11t) = 0.267949192431123 * (9s)
(9s)^2 + (0.267949192431123)^2 * (9s)^2 = 50
(9s)^2 * (1 + 0.071796769724491) = 50
(9s)^2 = 46.650635094611
9s = ± 6.83012701892219
s = 9 ± 6.83012701892219 choose the minus
s = 2.16987298107781
(11t)/(6.83012701892219) = 0.267949192431123
t = 12.8301270189222
B is at (2.16987298107781, 12.8301270189222)
Distance (0,0) to B is √(s^2 + t^2)
OB = 13.012321394574
plotting a circle of that radius centered at the origin indeed intersects B.
https://www.desmos.com/calculator/j8fmiruxwz

Posted by Larry
on 20240215 11:48:15 