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Example - 3 : Prove that any four vertices of a regular pentagon lie on a circle.

Give : ABCDE is a regular pentagon.

TO Prove : A, B., C and E lie on a circle.

Construction : AC and BE are joined

Proof :

Statement	Reason
1. In	1. Angles of a regular pentagon are equal .Sides of a regular pentagon are equal common
2.	2. S A S
3.	3. c.p.c.t.
4. A, B, C, E are cyncyclic	4. Angles in the same segment of a circle are equal

Example - 4. In the given figure, AB is a diameter of a circle with centre O. A circle is described on OA as diameter. A chord AD of the bigger circle intersects the smaller circle at C. Prove that BD = 2 OC.

Solution :