Question

Prove that a parallelogram inscribed in a circle is a rectangle. [2 MARKS]

Answer 1

Concept: 1 Mark
Application: 1 Mark

In the parallelogram ABCD,

$\angle A=\angle C$.....(i) (Since opposite angles of a parallelogram)

But, $\angle A+\angle C={180}^{\circ }$ (sum of opposite angles in a cyclic quadilateral is ${180}^{\circ }$)

$\angle A+\angle A={180}^{\circ }$...... [from (i)]

$2\angle A={180}^{\circ }$

$\angle A={90}^{\circ }$

But, a parallelogram, one of whose one angle is ${90}^{\circ }$, is a rectangle.

$\therefore$ ABCD is a rectangle.