How do I find the area of an isosceles trapezoid circumscribed about a circle when I know the lengths of the bases (8 and 18) but do not know the radius of the circle? Thanks.

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- December 4th 2007, 04:17 AMgarrett88Area of an Isosceles Trapezoid
How do I find the area of an isosceles trapezoid circumscribed about a circle when I know the lengths of the bases (8 and 18) but do not know the radius of the circle? Thanks.

- December 4th 2007, 04:46 AMcolby2152
- December 4th 2007, 05:23 AMgarrett88
No, not given. Either leg of the trapezoid is also the hypotenuse of a right triangle that has the height of the trapezoid as one of the two legs of that right triangle. I don't know if there is a theorem for this but it seems that if I draw two tangents to the circle from any exterior point, and I'll choose a vertex of the trapezoid as my exterior point, those two tangents must be of equal length, 4 and 4 from the top vertex and 9 and 9 from the bottom one. If that's true, then the hypotenuse is 9+4 = 13 and the bottom leg is 5, so the other leg (which is also the altitude of the trapezoid) is 12. Thus the area is 1/2 x 12 (8 + 18). or 216. Would that be correct?

- December 4th 2007, 06:52 AMearboth