i) The two circles below intersect at 'P, Q' and lines through thiese points meet the. circles at 'A, B, C, D'. The lines 'A C' and 'B D' are not parallel. Prove that if 'A C' and BD are. of equal length, then 'ABCD' is a cyclic quadrilateral.
'(##VPU_TTT_MAT_X_P01_C02_E05_006_Q01##)'
ii). In the picture, the circles on the left and right intersect the middle circle at 'P, Q, R, S ,' the lines joining them meet the left and right circles at 'A', 'B, C, D'. Prove that 'A B C D' is a cyclic quadrilateral.
'(##VPU_TTT_MAT_X_P01_C02_E05_006_Q02##)'