Question

If a parallelogram is inspired in a circle then prove that it is a rectangle

Answer 1

Let ABCD is a ||gram We know that opposite angles of a ||gram are equal so angle A = angle C and angle B = angle D We know that sum of opposite angles of a cyclic quad is 180 Now angle A + angle C = 180 => angle A + angle A = 180 => 2 angle A = 180 => angle A = 90 => ABCD IS A ||gm with angle = 90 => ABCD is a rectangle