Mathematics

Problem

Two equal chords

AB

and

CD

of a circle with centre

O

are parallel to each other. a. (i) Prove that

\angle AOB = \angle COD

. b. (ii) Show that the line joining the mid-points of

AB

and

CD

passes through

O

. c. (iii) If each chord is

12\,\text{cm}

long and the perpendicular distance between the chords is

8\,\text{cm}

, calculate the radius of the circle.