A, B and C lie on a circle with centre O. The minor angle $AOB=104^\circ$, and C lies on the major

Question

A, B and C lie on a circle with centre O. The minor angle $AOB=104^\circ$, and C lies on the major arc AB. Find $\angle ACB$.[1] Find $\angle OAB$, showing your reasoning.[2] D is a point on the minor arc AB, distinct from A and B. A pupil claims that $\angle ADB=\angle ACB$. Explain why this is incorrect.[1]

Accepted Answer

(a) $52^\circ$ (b) $38^\circ$ (c) The angles are supplementary; $\angle ADB=128^\circ$.

Central and circumference angles

Central and circumference angles

Solution:

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