SOLUTION: An isosceles trapezoid is inscribed in a circle, the upper base is 12cm, the other base is 16cm, sides are 2xsqrt(2). What is the diameter of the circle? In class we worked out th

Question 1093304: An isosceles trapezoid is inscribed in a circle, the upper base is 12cm, the other base is 16cm, sides are 2xsqrt(2). What is the diameter of the circle?
In class we worked out that the height of this trapezoid is 2cm, and at home I understood that the acute angles are 45* because the sides of that triangle are equal and one angle is 90*. What to do next? (Please explain as simple as possible as english is not my first language)
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
We want the length of a diagonal(d) of the isosceles trapezoid
:
the 16cm base extends 2cm on either side( (16-12) / 2 )
:
14^2 + 2^2 = d^2
:
d = square root(14^2 + 2^2) = 14.14
:
we are given
:
1) the equal sides of trapezoid, a = 2 * square root(2)
2) bases b = 16, c = 12
:
let s = (a + d + c) / 2 = (2*square root(2) + 14.14 + 12) / 2 = 14.48
:
Radius of circumscribed circle =
:
(a * d * c) / ( 4 * square root(s * (s-a) * (s-d) * (s-c) ) =
:
(2*square root(2) * 14.14 * 12) / ( 4 * square root( 14.48 * (14.48-2*square root(2) * (14.48-14.14) * (14.48-12) ) =
:
479.93 / 47.71 = 10.06
:
******************************************
Radius of circumscribed circle = 10.06 cm
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:
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