Question

p is the centre of the circle chord AB and CD intersect on diemeter at the point E if angle AEP congurnt angle DEP then proove that AB = CD

Answer 1

hey mate here is your solution
given:a circle with centre p
chord ab and cd intersect on diameter d at E
angle AEP=angleDEP
to prove:AB=CD
construction:draw pm perpendicular to AB and pn perpendicular to CD
prove:now in triangle MEP and triangle NEP
EP =EP(common)
angle AEP=angle DEP (given)
angle PME=angle PME(each90 degree)
there fore ∆MEP =~ ∆NEP (by AAS congruence)
there fore PM=PN (by CPCT)
since perpendicular distances from the center are equal
there fore the chords will be equal
AB=CD
hence, proved.
this will help you mate
see the diagram also