Question

abcd is a parallelogram the circle through a b c intersects cd produced at e prove that ae=ad

Answer 1

we have parraleogram abcd
such ad =BC
now aecb is a cyclic quadrilateral
so angle b+ angle c =180
and angle e+angle b=180
equating we get
angle b =angle c
now we join be and ac
now in triangle ace and bce
angle e =angle c
ec =ec
angle a= angle b[ angle in same segment)
so triangle ace and bce are congruent
ae =BC{ cpct}
BC =ad[ as abcd parraleogram]
so ae =ad
hence proved