Two diameters and of a circle with centre intersect at right angles at

MATHEMATICS · Multi-part · CBSE · Mathematics · Circles · Circles

Problem

Two diameters

AC

and

BD

of a circle with centre

O

intersect at right angles at

O

. The points appear around the circle in the order

A, B, C, D

. (i) Show that

\angle ABC = 90^{\circ}

. (ii) Prove that quadrilateral

ABCD

is a rectangle. (iii) If

OA = 7\,\text{cm}

, determine the perimeter and the area of rectangle

ABCD