In the diagram, $O$ is the centre of the circle through $A$, $B$, $C$ and $D$ and $TB$ i

Question

In the diagram, $O$ is the centre of the circle through $A$, $B$, $C$ and $D$ and $TB$ is the tangent to the circle at $B$. The diameter $AC$ and the chord $BD$ intersects at $X$. Given $\angle DCX = 32{}^\circ$ and $\angle OBC = 40{}^\circ$, calculate, stating your reasons clearly, $\angle OAB$, $\angle CXD$, $\angle ABT$, $\angle BAD$.

Accepted Answer

(a) $50^\circ$ (b) $98^\circ$ (c) $40^\circ$ (d) $108^\circ$

Euclidean Geometry: Interior Angles and Circular Arc Relationships

Euclidean Geometry: Interior Angles and Circular Arc Relationships

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