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Hint – we use the property of Diagonals of rhombus which bisect perpendicular to each other.

We can draw a rhombus whose diagonals are 5.2 cm and 6.4 cm long by following the given procedure.

1. Draw a line segment AC = 5.2 cm.

2. Draw XY, the perpendicular bisector of AC.

3. From XY, cut-off OD = $\dfrac{1}{2}(6.4)$ = 3.2 cm.

4. Similarly, cut-off OB = $\dfrac{1}{2}(6.4)$= 3.2 cm.

5. Join AD, DCCB and BA.

Thus, ABCD is the required rhombus.

Note - In this type of problem, let any cyclic quadrilateral and apply the property of the circle with its circumferences & some geometric properties and we get a rhombus whose diagonals are 5.2 cm and 6.4 cm long.

We can draw a rhombus whose diagonals are 5.2 cm and 6.4 cm long by following the given procedure.

1. Draw a line segment AC = 5.2 cm.

2. Draw XY, the perpendicular bisector of AC.

3. From XY, cut-off OD = $\dfrac{1}{2}(6.4)$ = 3.2 cm.

4. Similarly, cut-off OB = $\dfrac{1}{2}(6.4)$= 3.2 cm.

5. Join AD, DCCB and BA.

Thus, ABCD is the required rhombus.

Note - In this type of problem, let any cyclic quadrilateral and apply the property of the circle with its circumferences & some geometric properties and we get a rhombus whose diagonals are 5.2 cm and 6.4 cm long.

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