ABCD is a parallelogram. If the radius of the circle passing through all the vertices of a parallelogram is 4cm, then the length of the diagonal AC is
Given a circle is passing through all the vertices of the parallelogram ABCD.
Therefore ABCD is a cyclic parallelogram
In a cyclic quadrilateral sum of opposite internal angles is 180∘.
i.e., ∠ABC+∠ADC=180∘
But in parallelogram opposite internal angles are equal i.e., ∠ABC=∠ADC
Using the above relations we get ∠ABC=∠ADC=90∘
A parallelogram with an internal angle of 90∘ is called rectangle.
Since ∠ADC=∠ABC=90∘, ADC and ABC are semicircles as angle in a semi-circle is 90∘.
AC is the diameter of the circle.
AC = 2(radius) = 8 cm