2026-09-10T00:15:05.620071 image/svg+xml Matplotlib v3.10.9, https://matplotlib.org/ © EAGLE BEACON GLOBAL Use the diagram to answer both parts of this ques...
Question 1 Report
Use the diagram to answer both parts of this question.
Points \(A\), \(B\) and \(C\) lie on a circle with centre \(O\). Point \(B\) is on the major arc, and angle \(AOC = 128^{\circ}\).
(i) Work out angle \(ABC\). Give a reason for your answer.
(ii) Point \(D\) lies on the minor arc \(AC\). Work out angle \(ADC\).
Answer Details
For points on the same circle, the angle at the centre is twice the angle at the circumference standing on the same chord \(AC\). Point \(B\) is on the major arc, so \(\angle ABC\) stands on the minor arc \(AC\):
\[\angle ABC=\frac{128^\circ}{2}=64^\circ\] [M1 A1]
Points \(A,B,C,D\) form a cyclic quadrilateral, so opposite angles total \(180^\circ\). Therefore
\[\angle ADC=180^\circ-64^\circ=116^\circ\] [A1]
Thus \(\angle ABC=64^\circ\) and \(\angle ADC=116^\circ\).
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