MathDB

Let

ABCD

be an inscribed quadrilateral. Let the circles with diameters

AB

and

CD

intersect at two points

X_1

and

Y_1

, the circles with diameters

BC

and

AD

intersect at two points

X_2

and

Y_2

, the circles with diameters

AC

and

BD

intersect at two points

X_3

and

Y_3

. Prove that the lines

X_1Y_1, X_2Y_2

and

X_3Y_3

are concurrent.
Maxim Didin

M2600