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In the above figure, seg AB is a diameter of a circle with centre P. C is any point on the circle. seg CE ⊥ seg AB. Prove that CE is the geometric mean of AE and EB. Write the proof with the help of the following steps:

a. Draw ray CE. It intersects the circle at D.

b. Show that CE = ED.

c. Write the result using the theorem of the intersection of chords inside a circle. d. Using CE = ED, complete the proof.

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