In a circle with centre

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

Problem

O

, the chords

AB

and

CD

are equal in length. They subtend central angles

\angle AOB=(3x+20)^{\circ}

and

\angle COD=(5x-40)^{\circ}

O

. A third chord

EF

subtends a central angle of

70^{\circ}

. (i) Find the value of

x

. (ii) Using the value of

x

, determine the numerical measures of

\angle AOB

and

\angle COD

. (iii) Compare the lengths of chords

AB

CD

and

EF

, giving suitable reasons for every step of your comparison.