#### (a) In the figure (i) given below, chords AB, BC, and CD of a circle with centre O are equal. If ∠BCD = 120°, find

(i) ∠BDC

(ii) ∠BEC

(iii) ∠AEC

(iv) ∠AOB.

Hence Prove that AOAB is equilateral.

(b) In the figure (ii) given below, AB is a diameter of a circle with centre O. The chord BC of the circle is parallel to the radius OD and the lines OC and BD meet at E. Prove that

(i) ∠CED = 3 ∠CBD

(ii) CD = DA.

**Solution:**

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