NECO 2024 · Paper 1 · Q35

Circle geometry

In the diagram, $A$ , $B$ , $C$ and $D$ are points on a circle with centre $O$ , and $BA$ is produced to $M$ . If $\angle MAD = 82^\circ$ and $\angle ADO = 74^\circ$ , find $\angle ABO$ .

Worked solution (try it first)

$OA = OD$ (radii), so $\angle OAD = \angle ODA = 74^\circ$ .
$BAM$ is a straight line: $\angle BAD = 180^\circ - 82^\circ$
$= 98^\circ$ , so $\angle BAO = 98^\circ - 74^\circ$
$= 24^\circ$ .
$OA = OB$ (radii), so $\angle ABO = \angle BAO = 24^\circ$ , option A.

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