In the picture, all sides of a rhombus are tangents to a circle.

Draw this picture in your notebook.

Steps of construction:

1. Draw a circle of radius 2 cm [as diameter is 4 cm] with center O.

2. Draw a horizontal line XOY, through O

3. Draw ∠XOA = 70°, ∠XOB = 70° , ∠YOC = 70° and ∠YOD = 70°, such that points A, B, C and D lie on circumference.

4. Draw tangents from points A, B, C and D on the circle, such that they form a rhombus PQRS

Now, let's verify ∠CQD = 40°

In ΔCOQ and ΔDOQ

∠COQ + ∠CQO + ∠OCQ = 180° [By angle sum property of triangle]

As, ∠COQ = 70°( By construction)

And ∠ OCQ = 90° [Tangent at any point is perpendicular to the radius at the point of contact]

⇒ ∠CQO = 20°

Similarly, ∠DQQ = 20°

⇒ ∠CQO + ∠DQO = 40°

⇒ ∠CQD = 40