Mathematics

Problem

In a circle, two chords

AB

and

CD

are equidistant from the centre

O

. The length of

AB

(3x - 4)\,\text{cm}

and the length of

CD

(x + 8)\,\text{cm}

. A third chord

EF

is equal in length to

CD

and subtends a central angle of

(2y + 20)^\circ

. The chord

AB

subtends a central angle of

100^\circ

. a. (i) Form two algebraic equations in

x

and

y

using the given information. b. (ii) Solve the equations to find the values of

x

and

y

. c. (iii) Determine the common length of the three chords and the angle subtended by chord

EF

at any point on the circumference of the circle.