Question

Two chords AB and CD of the same circle are parallel to each other.P is the centre of the circle .Show that angle CPA=angle DPB
Note: Both chords AB and CD are on the same side of the circle.

Answer 1

Answer:

In ∆APB angleBAP=angleABP

{Angle opposite to equal side are equal }

Say=x

Similarly

anglePCD=anglePDC

Say =y

Now PAB=PDC

{ALTERNATE INTERIOR ANGEL}

X=y

Angle BPD=2x

Exterior angle property

AngelAPC=2x

BOTH EQUAL TO 2X SO THEY ARE EQUAL