if two equal chords AB and CD meet at point P when extended, prove that the secant segment AP and CP are equal

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if two equal chords AB and CD meet at point P when extended, prove that the secant segment AP and CP are equal

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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thanks how do you draw pictures on here?
use the draw facility below

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This is the picture i have for the question
hhmmm - i'm searching my memory with this one. if we can show that AC is parallel to BD then we can use similar triangles
yeah - thats basically the same as mine
Thanks i thought so...
i'm pretty sure they are parallel but not sure why!
Im not sure why as well thankf for the help
To Prove this you need to show that angle A = angle C since the chords are equal, arc AB = arc CD angle A = arc BC/2 angle C = arc AD/2 arc BC = arc CD + arc BD arc AD = arc AB + arc BD using substitution you can show that: arc BC = arc AD, therefore showing that angle A = angle C
Thank you

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