1.1. A car company is making a design for a new metal logo as shown in the image below.

Points A, B, C and D all lie on the circumference of a circle.  AB, AC, AD, BC, and CD are chords with AB = CD. The company wishes to have lines AB:BC:AC in the ratio 2:4:5.

The machine which makes the logo requires the angle ABC to be input accurate to
1 decimal place.

Calculate the angle ABC that should be input into the machine.

1.2. The acceptable error range of angle CAD is 1 degree. If a logo is tested and found to be outside of this range the machine requires calibration.

Find the acceptable range for ${x}^{^{\circ}}$ to 1 decimal place

1.3. Given that the company wishes BC to be 1 inch, use the angles correct to 1 decimal place found in parts (a) and (b) to calculate the area of the quadrilateral ABCD.