The two diagonals of a cyclic quadrilateral
EFGH are EG and FH while
the respective lengths of its adjacent sides EF and FG are 2 and 5.
It is known that Angle EFG = 60o
and the area of the quadrilateral is 4√3.
Determine the sum of the lengths GH + HE.
Let e = |GH| and g = |HE|.
Area = 4*sqrt(3)
= (1/2)|EF||FE|sin(60) + (1/2)eg*sin(180-60)
eg = 6
|EG| = |EF|^2 + |FG|^2 - 2|EF||FG|cos(60)
= e^2 + g^2 - 2eg*cos(180-60)
19 = e^2 + g^2 + eg
25 = 19 + eg = (e+g)^2
|GH|+|HE| = 5
One of the two possible quadrilaterals is an
Posted by Bractals
on 2007-10-21 14:02:43