Prove that a parallelogram inscribed in a circle is a rectangle. [2 MARKS]
Concept: 1 Mark
Application: 1 Mark
In the parallelogram ABCD,
∠A=∠C.....(i) (Since opposite angles of a parallelogram)
But, ∠A+∠C=180∘ (sum of opposite angles in a cyclic quadilateral is 180∘)
∠A+∠A=180∘...... [from (i)]
2∠A=180∘
∠A=90∘
But, a parallelogram, one of whose one angle is 90∘, is a rectangle.
∴ ABCD is a rectangle.