Question 13 (continued)

(c) The points A, B, C and D lie on a circle of radius r, forming a cyclic

quadrilateral. The side AB is a diameter of the circle. The point E is chosen on the diagonal AC so that DE ⊥AC.Letα=∠DAC and β=∠ACD.

(i) Show that AC =2r sin (α+β).

(ii) By considering ABD, or otherwise, show that AE =2r cosαsinβ. (iii) Hence, show that sin (α+β) =sinαcosβ+sinβcosα.

End of Question 13

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