Draw a circle with centre O and points A,B,C on its circumference. The measure of ∠ACB is 38∘.
The measure of the central angle ∠AOB is (5x−8)∘. A fourth point D is chosen on the circle such that the chord AD is equal to the chord AB.
(i) Find the measure of arc AB.
(ii) Using the result of part (i), calculate the value of x and hence find ∠AOB.
(iii) Prove that arcs AB and AD are equal.
(iv) Hence determine the measure of ∠AOD.}],