A ring of 10 cm in diameter is suspended from a point 12 cm vertically above the centre by six equal strings.?

The strings are attached to the circumference of the ring at equal intervals, thus keeping the ring in a horizontal plane. The cosine of the angle between two adjacent string is...


A) 2/sqrt(13);


B) 313/338;


C) 5/sqrt(26);


D) 5 sqrt(651)/338;


Kindly explain your answer...

A ring of 10 cm in diameter is suspended from a point 12 cm vertically above the centre by six equal strings.?
The answer is B).


The 6 strings and the 6 ring chords between every 2 suspension points are edges of a regular hexagonal pyramid with a base edge length of 5 (the inscribed regular hexagon's side length is equal to the radius - half of ring's diameter 10) and altitude 12. The right triangle with legs radius (5) and altitude (12) yields the lateral edge's length of 13 and the cosine law, applied to a lateral face (isosceles triangle with sides 5, 13 and 13) yields the answer:


(13² + 13² - 5²)/(2*13*13) = (338 - 25)/338 = 313/338

bottle palm