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B4nn3d
And once you've worked out what CP^2 is in terms of a^2 b^2 and a dot b, then you can just let a and b be at right angles to each other, making a right angled triangle, and hence a dot b = 0, and you can show CP^2 = AP^2.
:. |CP| = |AP| as required for the last part of the question.
:. |CP| = |AP| as required for the last part of the question.