Question

7. If diagonals of a cycle quadrilateral are diameters of the circle through the vertices of
the quadrilateral, prove that it is a rectangle​

Answer 1

Answer:

Let ABCD be a cyclic quadrilateral having diagonals BD and AC intersecting at point O

<BAD = 1/2 <BOD = 180°/2 = 90°

<BAC + <BCD = 180°

<BCD = 180° - 90°

<ADC = 1/2<AOC = 1/2 × 180° = 90°

<ADC + < ABC = 180° ( Cyclic quadrilateral)

<ABC = 180° - 90°

= 90°

Therefore,it is a rectangle