A trapezoid of ABCD vertices is inscribed in a circle, with radius R, being AB = R and CD = 2R and BC and AD being non-parallel sides. The bisectors of the internal trapezoidal angles, so that the bisector of  intercepts that of Dˆ at point Q, that of B intersects that of C N at point N and that of C ˆ intercepts that of Dˆ at point M. Knowing that the points M, N and Q are inside the ABCD trapezoid and that point P is the intersection of the Bˆ and Aˆ guidelines, determine the relationship between the areas of the MNPQ and ABCD polygons. Ans .: 1/9.
I tried a lot to do this, but everytime I found a segment with negative size Please, can someone help me? Thanks for antetion.
The hint.
$CD$ is a diameter of the circle, which gives $AB=AD=BC=R$.