MathDB

Let

XY

be a segment, which is a diameter of a semi-circle. Let

Z

be a point on

XY

and 9 rays from

Z

are drawn that divide

\angle XZY=180^{\circ}

into

10

equal angles. These rays meet the semi-circle at

A_1, A_2, \ldots, A_9

in this order in the direction from

X

Y

. Prove that the sum of the areas of triangles

ZA_2A_3

and

ZA_7A_8

equals the area of the quadrilateral

A_2A_3A_7A_8

M2787