Q. 45.0( 5 Votes )

# We draw a quadrilateral ABCD having AB = 4 cm, BC = 7 cm CD = 4 cm, ∠ABC = 60°, ∠BCD = 60°. Let us draw the circle circumscribing ΔABC and write what other characteristics we observe.

Answer :

Steps of Construction:

1. Construct quadrilateral ABCD of given dimensions.

2. We join A to C.

3. Draw perpendicular bisector of AB.

4. Draw perpendicular bisector of BC.

5. The point of intersection is the circumcenter. Name it as O.

6. With O as center and OC as radius, draw a circle.

7. The circle passes through A,B and C and is thus the circumcircle of this triangle.

We observe that ABCD is a cyclic quadrilateral as all the points A,B,C and D lie on the circle.

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